Write the equation of lowest degree with real coefficients if two of its roots are -1 and 1+i. The answer is x^3-x^2+2=0. I don't understand why

66,295 questions
1. Math

Write the equation of lowest degree with real coefficients if two of its roots are -1 and 1+i. The answer is x^3-x^2+2=0. I don't understand why.

asked by Bethany on April 1, 2016
2. college pre-calculus

what is the equation of lowest degree with real coefficients if two of its roots are -1 and 1+i? A. x^3+x^2+2=0 B. x^-x^2-2=0 C. x^3-x+2=0 D. x^3-x^2+2=0 e. none of the above i don't get it is it (x+1) (1+i)

asked by kyle on January 6, 2015
3. Math

Create a 3rd degree polynomial with real coefficients that has roots -1 and 4i. Write your answer in form ax^3 + bx^2 + cx+ .

asked by Anon on May 24, 2013
4. Math

Create a 3rd degree polynomial with real coefficients that has roots -1 and 4i. Write your answer in form ax^3 + bx^2 + cx+ d .

asked by Anon on May 24, 2013
5. Math

A polynomial function f(x) has degree 6 and has real coefficients. It is given that 3, 2, 11−3i, and 11+28i are roots of f(x). What is the sum of all the roots of f(x)?

asked by Crow on June 10, 2013
6. Math (Algebra)

For each degree 17 polynomial f with real coefficients, let sf be the number of real roots (counted with multiplicity). Let S be the set of all possible values of sf. What is |S|?

asked by Shin on May 7, 2013
7. Math

Write a polynomial of the lowest degree with real coefficients and with zeros 6-3i (multiplicity 1) and 0 ( multiplicity 5)

asked by Kayla on November 9, 2016
8. factoring

can this equation be factored further? y= x^4+2x^3+4x^2+8x+16 Not in the real number system. If you plot the function, you will see the minimum is at x=-1.1 (approx) and y is positive. At no x does the function equal zero, so there are no real roots, which

asked by kristie on July 26, 2006
9. Precalculus

"Show that x^6 - 7x^3 - 8 = 0 has a quadratic form. Then find the two real roots and the four imaginary roots of this equation." I used synthetic division to get the real roots 2 and -1, but I can't figure out how to get the imaginary roots. I checked

asked by Emily on September 20, 2009
10. Alegbra 2

Use the rational root theorem to list all possible rational roots for the equation. X^3+2x-9=0. Use the rational root theorem to list all possible rational roots for the equation. 3X^3+9x-6=0. A polynomial function P(x) with rational coefficients has the

asked by Chelsey on January 26, 2018
11. Pre Calc

Write an equation to a polynomial function that has the following properties: Fourth degree equation Lead coefficient is -2 Two negative real roots and one positive real root The positive real root has multiplicity of 2

asked by Anonymous on December 1, 2015
12. pre calc

A polynomial f(x) with real coefficients and leading coefficient 1 has zeros 6 + 4i, -5 + i and degree 4. Express f(x) as a product of quadratic polynomials with real coefficients that are irreducible over R. ive done this problem every which way i could.

asked by gabs on May 20, 2011
13. Pre-Calc/Trig...

Helpp needed, this is sort of confusing me. Describe the nature of the roots for this equation. 2x^2-x+1=0 A. Two real, rational roots B. Two real, irrational roots C. One real, double root D. Two complex roots

asked by Anonymous on October 17, 2014
14. pre-calculus math

A polynomial f(x) with real coefficients and leading coefficient 1 has the given zeros and degree. Express f(x) as a product of linear and/or quadratic polynomials with real coefficients that are irreducible over . 3, −3 − 2i;    degree 3

asked by deena on September 29, 2017
15. algebra 3

Find a polynomial of lowest degree with only real coefficients and having the given zeros. -2+i, -2-i, 3, -3

asked by jordan on September 24, 2009
16. algebra

if a quadratic equation with real coefficents has a discriminant of 10, then what type of roots does it have? A-2 real, rational roots B-2 real, irrational roots C-1 real, irrational roots D-2 imaginary roots

asked by brroooee on March 26, 2015
17. Algebra

Can someone please explain how to do these problems. 1)write a polynomial function of least degree with intregal coefficients whose zeros include 4 and 2i. 2)list all of the possible rational zeros of f(x)= 3x^3-2x^2+7x+6. 3)Find all of the rational zeros

asked by Marissa on August 10, 2007
18. Cubic Equations

I have three that I need help with if possible. 1. Solve 2x^3 - 3x^2 = 6x - 9 2. Find all real and imaginary roots of the polynomial equation 3x^4 - x^3 + 4x^2 - 2x - 4=0 3. Find a cubic equation with integral coefficients and roots 3i and -5.

asked by Belinda on January 8, 2012
19. Algebra

Find the polynomial function P of the lowest possible degree, having real coefficients, with the given zeros. 3+2i, -2 and 1

asked by Tim on March 10, 2011
20. maths2

Use the discriminant to determine the number of real roots the equation has. 7x2 + 3x + 1 =0 A. One real root (a double root) B. Two distinct real roots C. Three real roots D. None (two imaginary roots)

asked by mdan on October 7, 2013
21. mathematics

Use the discriminant to determine the number of real roots the equation has. 3x2 – 5x + 1 =0 A. One real root (a double root) B. Two distinct real roots C. Three real roots D. None (two imaginary roots)

asked by mdan on October 7, 2013
22. Math

A math teacher wrote x^2+bx+c=0 on the board and asked students to find the two real roots. Alice miscopied one of the coefficients and found that 1 and 4 were the roots. Andy miscopied a different coefficient and found that -2 and 3 were the roots.

asked by Devin on February 25, 2012
23. Algebra II

Which describes the number and type of roots of the equation x^2 -625=0? A. 1 real root, 1 imaginary root B. 2 real roots, 2 imaginary roots C. 2 real roots D. 4 real roots. I have x^2 = 625 x = 25 answer: 2 real roots (25 or -25) Is this correct? Thanks

asked by Lucy on March 16, 2008
24. Algebra 2

Find a real plynomial equation with real coefficients that has the given roots. 3-2i, 3+2i Should I just make it [x- (3-2i)][x + (3-2i)] then multiply it out and there's my answer? angela, thanks for your help how did you get the 56.80 from my problem.

asked by Angela on December 20, 2006

I have two questions that I don't understand and need help with. 1. information is given about a polynomial f(x) whose coefficients are real numbers. Find the remaining zerosof f. degree 4, zeros i;9+i 2. form a polynomial f(x) with real coefficients

asked by Paul on December 27, 2012
26. Algebra 2

Find a third-degree polynomial equation with rational coefficients that has roots -1 and i+1

asked by Ryan on March 13, 2015
27. Precalculus

Write the simplest polynomial equation with real coefficients having roots -i and 4. I have noooooo idea how to even start this one :( I thought you could start backwards with synthetic substitution but it didn't work. Any help on this is greatly

asked by Emily on September 3, 2009
28. Algebra

If a quadratic equation with real coefficients has a discriminant of 225, the what type of roots does it have?

asked by Zayn on March 26, 2015
29. Math - Fundamental Theorem

We can actually use the Zeros Theorem and the Conjugate Zeros Theorem together to conclude that an odd-degree polynomial with real coefficients must have atleast one real root (since the non-real roots must come in conjugate pairs). But how can we get the

asked by Sean on October 12, 2009
30. math

The function f(x)=x4−15x3+81x2−201x+182 has four complex roots, one of which is 3−2i. What is the sum of all real and imaginary coefficients of these roots?

asked by ayan on April 16, 2013
31. algebra

if a quadratic equation with real coefficients has a discrimiant of 225, then what type of roots doe it have? imaginary, rational or irrational?

asked by brroooee on March 26, 2015
32. maths

Show that the equation (1) divided by (x+1) - (x)divided by (x-2)=0 has no real roots Well, to begin, start with 1/(x+1-x). The x's cancel out because they are opposite signs, so now you have 1/1, or just 1. Then, you are dividing 1 by (x-2). In order for

asked by rochelle on January 28, 2007
33. Algebra

Write a polynomial of least degree with real coefficients and with the root -6-8i. Write your answer using the variable x and in standard form with a leading coefficient of 1. Thanks, I have no idea!

asked by Mom on September 16, 2015
34. Alg II

I'm working with finding roots of polynomial equations with degrees of 3 or higher. I have the equation r(x)=x^4-6x^3+12x^2=6x-13 I used a graphing calculator to find the real roots of 1,-1 Then I did synthetic using -1, and I ended up with the equation

asked by Josh on January 20, 2010
35. Alg II

I'm working with finding roots of polynomial equations with degrees of 3 or higher. I have the equation r(x)=x^4-6x^3+12x^2=6x-13 I used a graphing calculator to find the real roots of 1,-1 Then I did synthetic using -1, and I ended up with the equation

asked by Josh on January 20, 2010
36. trig

How do you write the quadratic equation with integer coefficients that have the roots 7-3i and 7+3i?

asked by KELLY on December 21, 2010
37. MATH

write, in extended form, a polynomial(with real coefficients) of degree 3, with solutions 2,2-i.

asked by Jill on July 26, 2011
38. Math

Which describes the number and type of roots of the equation x^2-625=0? A)1 real root, 1 imaginary root B)2 real roots, 2 imaginary roots C)2 real roots D)4 real roots I went with A sqrt x^2= x (which would be the imaginary) and sqrt 625= 25 (the real)

asked by Jon on February 20, 2008
39. algebra

write a fourth degree polynomial function with real coefficients that has -3,1/5, and 4+i as zeros and the y intercept of (0,5)

asked by james on March 28, 2014
40. Pre-Calculus/Trig Check please and help

Could someone please check the first one and help me with the second one. I'm stuck-Thank you 1.What are theroots of the following polynomial equation? (x+2i)(x-5)(x-2i)(x+8) = 0 I think the roots are -2i,5,2i,-8-you take out the roots as opposites of what

asked by Tabitha on September 5, 2011
41. Chemistry

When the equation below is balanced and all coefficients are in the lowest, whole number ratio, the coefficients are: C2H6 + O2 ¨ CO2 + H2O I am currently doing an online worksheet to improve in chemistry and I am not quite understanding how to find the

asked by Anonymous on July 1, 2016
42. Algebra

The function f(x)=x^4−10x^3+40x^2−80x+64 has four complex roots, one of which is 2−2i. What is the sum of all real and imaginary coefficients of these roots? i here is imaginary unit i.e. i^2 = -1

asked by Stranger on March 18, 2013
43. algebra

3x^4 + 5x^2 - 2 = 0 give imaginary and real roots rational roots theorem factors of (+-)p/q are possible rational zeros of function f where the coefficients of f are integers. how do you go about solving this?

asked by jack on August 7, 2017
44. Maths

The function f(x)=x^4−15(x^3)+81(x^2)−201x+182 has four complex roots, one of which is 3−2i. What is the sum of all real and imaginary coefficients of these roots? Details and assumptions i is the imaginary unit, where i2=−1.

asked by OIan on April 16, 2013
45. Math

Determine for what value(s) of d the quadratic equation 5x^2-10x+d = 0 has i) real and distinct roots ii)real and equal roots iii)non-real roots This is what I did to solve for A. 5x^2-10x+d = 0 b^2-4ac = 0 (-10)^2-4(5)(d) = 0 100-20d = 0 -20d = -100 d = 5

asked by -Untamed- on December 5, 2011
46. College math

Which statement describes the quadratic equation 6x^2-4x+1=0,correctly? A. it is one completed real root? B. It is two complete complex roots? C. It is two unequal real roots? Please help me with this

asked by Cassandra on March 17, 2014
47. Math (Algebra)

f(x)=x^4+ax^3+bx^2+cx+d and has real coefficients. If two of the roots are 4−i and 2+3i, what is the value of a+b+c+d?

asked by Shin on May 21, 2013
48. Algebra2

Find the polynomials roots to each of the following problems: #1) x^2+3x+1 #2) x^2+4x+3=0 #3) -2x^2+4x-5 #3 is not an equation. Dod you omit "= 0" at the end? #2 can be factored into (x+1)(x+3) = 0, so the roots are x=-1 and -3. #1 Use the quadratic

asked by Haylee on May 13, 2007
49. Pre Cal

Use Descartes’ Rule of Signs to find the number of possible positive, negative, and nonreal roots for the equation, 4x^3+7x^2+7x+3=0 a. 0 positive, 0 negative, 3 non real roots b. 0 positive, 1 or 3 negative, 0 or 2 non real roots c. 0 positive, 1 or 3

asked by Jackson on August 17, 2016
50. AMath

Write a polynomial function of minimum degree in standard form with real coefficients whose zeros include those listed 2, 3 and i.

asked by Brenda on October 27, 2010
51. Algebra 2

How would you write a polynomial function with rational coefficients so that P(x)=0 has the given roots? The given roots are -2,-2,3,5

asked by Jess on February 14, 2016
52. Math

Find the discriminant for the quadratic equation f(x) = 5x^2 - 2x + 7 and describe the nature of the roots. discriminant is 144, one real root discriminant is -136, two complex roots

asked by Jass on February 27, 2017
53. pre cal

Write a polynomial function of minimum degree with real coefficients whose zeros include those listed. Write the polynomial in standard form. 3, -13, and 5 + 4i Urgently need help

asked by Jorgeeee on June 29, 2014
54. Algebra

How can you tell an equation's real or imaginary roots just from its graph, without knowing the equation? I have to look ath the graph of a parabola, absolute value, and a negative third degree equation and do so? Are there any links that could explain

asked by Anneliese on November 2, 2009
55. Chemistry

When the equation below is balanced and all coefficients are in the lowest, whole number ratio, the coefficients are: Bi + O2 ¨ Bi2O3

asked by Anonymous on July 1, 2016
56. Chemistry

When the equation below is balanced and all coefficients are in the lowest, whole number ratio, the coefficients are: Bi+O2⟶Bi2O3

asked by Driyah on March 16, 2017
57. Algebra

Can someone tell me how they got the answer? Find a polynomial equation with real coefficients that has the given roots. 4i, sqrt5 my answer: x^4-22x^2+80=0 correct answer: x^4+11x^2-80=0

asked by Joey on April 5, 2008
58. Math

Given that the equation x(x-2p)=q(x-p) has real roots for all real values of p and q. If q=3, find a non-zero value for p so that the roots are rational.

asked by Majek on March 16, 2017
59. math

Write a quadratic equation with real coefficients if one of the solutions is -5 + 7i

asked by Jill on April 7, 2012
60. Algebra 2

I am trying to factor a 4th degree polynomial that does not have any rational roots. I need to somehow get it factored into two quadratics. Anyone know of a method to use. 3x^4 - 8x^3 - 5x^2 + 16x - 5 Two of the irrational roots are 1.135.. and 0.382.. but

asked by Brenda on March 9, 2007
61. how many solutions are real?

hi, I am stuck on this question. y=x^2+4x and y^2= 25x^2+20x+3 how many of the solutions are real? and how many of the real roots are positive and how many are negative? thank you for any suggestions I suggest you solve for the roots. y=x(x+4) At y=0, what

asked by wi on May 21, 2007
62. math

How do I write complex and real roots? For example, if the real roots are 1, -1 and the complex roots are -i, i how do I write those down? It'd be x:1, x:-1, x:-i, x:i, correct? Or am I wrong?

asked by Ortega on April 6, 2015

please help me solve these 1. 2√5/8 + 4√3/8 - 1/2√68 2. √4k-5 +1=8 (the radical sign goes over 4k-5) 3. (x+4)*2 /3 =8 4. Write the value of the discriminant of each equation. Then use it to decide how many different real-number roots the equation

asked by jenna on May 6, 2011
64. algebra

find a third degree polynomial equation with coefficients that has roots -4 and 6+i possible answers x^3-8x^2-11x+148=0 x^3-8x^2-12x+37=0 x^3-12x^2+37x=0 x^3-8x^2-11x=0

asked by jayson on November 12, 2012
65. ALGEBRA CHECK ANSWERS

Solve each equation by graphing the related function. If the equation has no real-number solution, write no solution. NOTE: when I write + it has a minus on the bottom too x^2+7=0 a. x= +7 b. x = +3.5 c. x= 0 d. no solution *** 3x^2=0 a. +3 b. +1/3 c. 0

asked by a on April 4, 2017
66. maths

find the roots of the equation X(square)+7x equal to 0.(b)write down the equation whose roots are -2 and 5. I will be happy to critique your thinking. Write the equation, and solve. In the second, hint: (x+2) is one factor.

asked by nikita on June 6, 2007
67. chemistry

Write the net ionic equation for the following molecular equation. 3FeI2 (aq) + 2(NH4)3PO4 (aq) --> Fe3(PO4)2 (s) + 6NH4I (aq) (Use the lowest possible coefficients. Use the pull-down boxes to specify states such as (aq) or (s). If a box is not needed,

asked by Hope S. on September 27, 2019
68. Algebra

I need help, my teacher says that I'm half way right with this but not fully what am I missing I'm confused. The criteria for the quadratic equation as i written is: y>0 is real roots y=0 is real and equal roots y

asked by Angel on November 8, 2012
69. Algebra 2

Q: Write a quadratic equation with integral coefficients whose roots are -6+i and -6-i My Answer: x^2+12x+37 (first) sum=-12 product=37 (then) write equation using formula x^2-(sum)x+product Is my work and answer correct?

asked by Bryan on March 21, 2016
70. chemistry

I have the chemical equation: CH4 + NH3 + O2 => HCN + H2O, I have to write a balanced equation using the lowest whole number coefficients, including the state of each compound -- HELP PLEASE http://www.daigger.com/equationsbalancer.jsp All are gases, even

asked by Desmond on May 8, 2007
71. Chemistry

Write a balanced chemical equation that represents the self-ionization of water. (Use the lowest possible coefficients. Include states-of-matter at 1 atm and 25°C in your answer.)

asked by Grace on April 2, 2014
72. math

write a polyoil equation ofleast degree for each set of roots +/-2i,3,-3.

asked by tashonda on September 19, 2011
73. Precalculus

Write a polynomial function of minimum degree in standard form with real coefficients whose zeros and their multiplicities include those listed. 2(multiplicity 2), -4(multiplicity 3)

asked by Anonymous on March 26, 2017
74. Precalculus

Write a polynomial function of minimum degree in standard form with real coefficients whose zeros and their multiplicities include those listed. 3(multiplicity 2), 5+i(multiplicity 1)

asked by Anonymous on March 26, 2017
75. algebra 2

Suppose the polynomial f(x) has the following roots: 1+6sqrt2, 2−sqrt6, and 6+sqrt2. If f(x) has only rational coefficients, the Irrational Root Theorem indicates that f(x) has at least three more roots. What are the three additional roots that f(x) must

asked by kayla on January 25, 2018
76. Math - Int Trig

Form a polynomial f(x) with real coefficients having the given degree and zeros 21) Degree: 4, zeroes: 2i and -3i 22) Degree: 3, Zeroes i and -10

asked by Lilly on May 15, 2014
77. Maths

q2) a) write the equation cos2x + 8cosx+9=0 in terms of cosx and show that for cosx it has equal roots q2b) show that there are no real roots for x. for q2 i have tried to do it but i get upto the bit 2(cosx+2)(2cosx+2)=0 and i don't know what to do next.

asked by PLEASE ANSWER I NEED HELP CHEERS!!!!!!!!!! on December 6, 2009
78. Math help please

In this problem you will use Rolle's theorem to determine whether it is possible for the function f(x) = 8 x^{7} + 7 x - 13 to have two or more real roots (or, equivalently, whether the graph of y = f(x) crosses the x-axis two or more times). Suppose that

asked by sheks on November 26, 2013
79. Math

determine the value(s) of k which the equation x^2+kx+9=0 will have a) two real roots b) 2 distinct roots I tried to find the discriminant but I didn't get the right answer.

asked by fatima on October 2, 2016

Use the value of the discriminant to determine the number and type of roots for the equation: (x^2+20=12x-16) 1 real, irrational 2 real, rational no real 1 real, rational

asked by Chels on November 3, 2007
81. Algebra

I need help with a few questions, please explain. 1. Write a polynomial function in standard form with zeros -1, -1, 6. 2. Find the roots of the equation x^3 – 3x^2 + x + 5 3. Describe the number and type of roots for the polynomial (how many real and

asked by |-/ on January 31, 2018
82. algebra

Determine the value(s) of k for which x^2+(k-2)x-2k=0 has equal and real roots. a x^2 + bx + c = 0 has two different roots if the discriminant D defined as: D = b^2 - 4 a c does not equal zero. If D = 0 then there is one root. That root is then real if b/a

asked by Shay on January 18, 2007
83. math

third-degree polynomial with real coefficients -4 -3

asked by Anonymous on March 24, 2013
84. Math

determine the value(s) of k which a quadratic equation x^2+kx+9=0 will have. a) two equal real roots b) 2 distinct roots I tried to find the discriminant but couldn't get the right answer

asked by Anonymous on October 2, 2016
85. pre calculus

use given info about a polynomial whose coefficients are real numbers to find the remaining zeros. Degree: 6 so I know there's at least 6 zeros:-5-isqrt7, 13 + 2ni, -5 - 3i (where n is a real number) any ideas??????

asked by amy on September 25, 2011
86. Chemistry

Write the balanced chemical equation for each of the following. (Use the lowest possible coefficients. Include states-of-matter at 1 atm and 25unknown_prefixC in your answer.) (b) the reaction of magnesium metal and hydrobromic acid

asked by Grace on April 2, 2014
87. Chemistry

Write the balanced chemical equation for each of the following. (Use the lowest possible coefficients. Include states-of-matter at 1 atm and 25unknown_prefixC in your answer.) (a) the dissociation of solid magnesium hydroxide in water

asked by Grace on April 2, 2014
88. Linear Algebra

Let R5[t] be the vector space of all polynomials in t of degree 4 or less with real coefficients. Which of the following subsets are subspaces? I know how to test if something is a subspaces, just not sure how to do it with for these polynomial equations.

asked by bdinh on October 22, 2013
89. Linear Algebra

Let R5[t] be the vector space of all polynomials in t of degree 4 or less with real coefficients. Which of the following subsets are subspaces? I know how to test if something is a subspaces, just not sure how to do it with for these polynomial equations.

asked by bdinh on October 22, 2013
90. Form a polynomial f(x) from coefficient and it's 0

Form a polynomial, f(x), with real coefficients having the given degree and zeros. Degree: 4; zeros: 6i and 7i I completely don't know what to do with this problem... if someone can solve and give a good explanation, I'd appreciate it. Thanks.

asked by Armando on May 30, 2011
91. pre-calculus

form a polynomial f(x) with real coefficients having the given degree and zeros. degree: 4; zeros: -1, 2, and 1-2i. I got an exam tomorrow, i would appreciate any kind of help, thank you.

asked by Hawra on March 13, 2010
92. Algebra

Find a polynomial function of lowest degree with rational coefficients that has the given numbers as some of its zeros. 2-i,sqrt2 f(x)= ? Thanks!

asked by Walker on October 1, 2016
93. Algebra

Find a polynomial function of lowest degree with rational coefficients that has the given numbers as some of its zeros. sqrt of 3, 4 Thanks!

asked by Jason on November 16, 2016
94. Algebra

Find a polynomial function of lowest degree with rational coefficients that has the given numbers as some of its zeros.    3-i,sqrt2 f(x)=??

asked by Gabby on October 26, 2016
95. pre-calculus

information is given about the polynomial f(x) whose coefficients are real numbers. find the real zeros of f: degree 4; zeros: i, 3+i

asked by hawra on March 13, 2010
96. calculus

form a polynomial with real coefficients have given degree and zeros. degree 5, zeros 9, -i; 8+i please show work

97. Calculus

Form a polynomial, f(x) with real coefficients having the given degree and zeros. Degree: 4 ; Zeros: 4i and 5i Really need help! don't know where to start.

asked by Mary on September 22, 2011
98. Algebra ll

Please help!! I do not understand any of this!! Form a polynomial f(x) with real coefficients having the given degree and zeros. Degree 4; zeros: 2, multiplicity 2; 3i

asked by Sherri on May 11, 2015
99. Math

Find a polynomial of degree 3 with real coefficients and zeros of -3, -1, and 4, for which f(-2) = 24.

asked by DeniseG on July 12, 2016
100. Math

find a polynomial of least degree(having real coefficients) with zeros: 5, -2, 2i

asked by Amber on September 27, 2012