
Use the rational root theorem to list all possible rational roots for the equation. X^3+2x9=0. Use the rational root theorem to list all possible rational roots for the equation. 3X^3+9x6=0. A polynomial function P(x) with rational coefficients has the

Please help find the rational roots of f(x)=4x^4  3x^3 + 2x^2 +x  3 another is f(x)=3x^3  2x^2 + x  1 I tried but still confuse please help really really need help Thank you very much!

Factor this polynomial: F(x)=x^3x^24x+4 Try to find the rational roots. If p/q is a root (p and q having no factors in common), then p must divide 4 and q must divide 1 (the coefficient of x^3). The rational roots can thuis be +/1, +/2 and +/4. If you

I have a few problems I need help with and also do have multiple choice. If I can have an explanation of how to get the answer that would be great. 1. Use the discriminant to determine whether the given equation has two irrational roots, two rational

How to factor x^3  3x^2 + 4 =0 Use D'Alembert's Rational Roots Theorem. Any rational roots of the form of p/q (p and q assumed to be relatively prime) must be such that p divides the constant term (in this case 4) and q divides the coefficient of the


I have a few problems I need help with and also do have multiple choice. If I can have an explanation of how to get the answer that would be great. 1. Use the discriminant to determine whether the given equation has two irrational roots, two rational

Use the Rational Root Theorem to list all possible rational roots for each equation. Then find any actual roots. x^3 + 2x^2 + 3x + 6 = 0 (8 points)

1) Find the roots of the polynomial equation. x^32x^2+10x+136=0 2) Use the rational root theorem to list all problem rational roots of the polynomial equation. x^3+x^27x4=0. Do not find the actual roots.

Radical and Rational Exponent find roots square roots of 12a^3/25=6a^3 3square roots 18/6=1 this is my answer am I right. check this for me it find the roots of the problem

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^32x^2+7x+6. 3)Find all of the rational zeros

List all possible rational zeros of... h(x)= 2x to the (4th power)  5x (to the third power) + 3x (to the 2nd power) + 4x  6 Use the Rational Roots Theorem. Any root of the form p/q with p and q relatively prime must be such that p divides 6 and q divides

Radical and Rational Exponent find roots square roots of 12a^3/25=6a^3 3square roots 18/6=1 check this for me it find the roots of the problem.

Radical and Rational Exponent find roots square roots of 12a^3/25=6a^3 3square roots 18/6=1 check this for me it find the roots of the problem.

1.) What are the possible rational roots of the function f(x) = 3x^4  x  2 2.) What are the rational roots of the following equation: x^3  4x^2  4x +16 = 0 Thank you for any help!

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?


Is this correct? Using Rational Roots Theorem, list all possible rational root of f(x) = 2x^3  3x^2 + 5x+6 Possible roots are p/a = +1, +2, +3, +6. +3/2

using the rational root theorem to list all possible rational roots of the polynomial equation x^3x^2x3=0 possible answers 3,1,1,3 1,3 33 no roots

List the possible rational roots of 2x^3 + 17x^2 + 23x  42 = 0 My answer: the possible rational roots are {±1, ±2, ±3, ±6, ±7, ±14, ±21, ±42. ±1/2, ±3/2, ± 7/2, ±21/2}. Correct?

Still looking at how to solve these... Both are cubic polynomials? 43x^3 + 13x^2 + 18x  456 = 0 DO I divide first by x1? 2x(3x+2)^2=312 Honestly: I would graph the equations and find the roots first. I don't see them off hand. graph y=43x^3 + 13x^2 + 18x

I HAVE THESE ANSWERS FOR THE PROBLEMS. COULD YOU DOUBLE CHECK PLEASE, THIS IS A PRACTICE QUIZ WHICH ISN'T A GRADE IT JUST HELPS ME GET READY FOR THE TEST. 1) a 2) b 3) d 4) a 5) d 1. Solve x^3 + 6x^2 + 13x + 10 = 0. a) –2 + 2i, –2 –2i, –2 b) 2 + i,

I have three questions: 1. What is the remainder of (x^3 + 2x^2  5x+4) /(x3) I think the answer is 34?? 2. Evaluate (4+5i)(2+2i) =4(2) +4(2i) + 5i(2) + 5i(2i) = 8 + 8i + 10i+10i^2(1) =2 + 18i 3. Using Rational Roots Theorem, list all possible rational

Find all possible rational roots using the rational root theorem. x^4  3x^2 + 12 = 0 Plus/minus 1, 2, 3, 4, 6, 12?

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

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

Could you please solve so I can double check my answers for the practice quiz? Thank You!! 1. Solve x^3 + 6x^2 + 13x + 10 = 0. a) –2 + 2i, –2 –2i, –2 b) 2 + i, 2 – i, –2 c) –2 + i, –2 – i, –2 d) 2 + 2i, 2 – 2i, –2 2. Find the


if a quadratic equation with real coefficents has a discriminant of 10, then what type of roots does it have? A2 real, rational roots B2 real, irrational roots C1 real, irrational roots D2 imaginary roots

how many roots does this polynomial have: f(x) = 5x^3 + 8x^2 4x + 3 and Of the possible rational roots, which ones are roots: ±1, ±(1/5), ±3, ± (3/5)

State the number of complex roots,possible number of real roots and possible rational roots for x^5  x^3  11x^2+ 9x+18=0

Given that the equation x(x2p)=q(xp) has real roots for all real values of p and q. If q=3, find a nonzero value for p so that the roots are rational.

List all possible rational zeros of each function. f(x)=4x^5+4x^29 Find all rational roots of each function f(x)=2x^3+x^2+8x+4

Find all possible rational roots using the rational root theorem. 3x^3 + 2x^2  1 = 0 plus/minus 1/3 and plus/minus 1?

A jewelry box is designed such that its length is twice its width and its depth is 2 inches less than its width. The volume of the box is 64 cubic inches. Use synthetic division to find the roots of the polynomial equation. Are the roots all rational

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

Hello, I have tried solving this using the rational roots theorem and none of the roots seem to be working. I'm trying to figure out where I went wrong. 3x^3 2x^2  7x  4 = 0

Find the polynomials roots to each of the following problems: #1) x^2+3x+1 #2) x^2+4x+3=0 #3) 2x^2+4x5 #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


use the rational root theorem to list the possible rational roots for each of the following equations f(x)=x^2+2x+1 f(x)=x^22x+5 f(x)=x^2+4x5

Prove that if p and q are rational and p is not equal to 0, the roots of the quadratic equations p x(square) + 2qx p +2q = 0 are rational.

list all the possible rational roots of P(x) given by the Rational Root Theorom. P(x)=4x^42x^3+x^212

how do prove that this equation has rational roots for all rational values of K 3x^2+kxk=3x

If a b c are non zero,unequal rational numbers then prove that the roots of the eqn (abc²) x²+ 3a²cx+b²cx6a²ab+2b²=0 are rational.

Use the Rational Theorem to list the possible rational roots. f(x)=x^2+2x+1 f(x)=x^22x+5 f(x)=x^2+4x5

List the possible rational roots of each equation. Then determine the rational roots. 6x^4+35x^3x^27x1 The answer in the back of the book is: 1/3 and 1/2 I know that I'm supposed to use Descartes rule of signs. I found that there was 1 positive zero

Find all the possible rational roots of f(x)= 4x^4  3x^3 +2x^2 + x 3 f(x) = 3x^3  2x^2 + x 1 Thank you so much:)

Find the rational roots of x^4+3x^3+3x^23x4=0. A.0,1 B.1,2 C.1,1 D.1,2

find all the possible rational roots of g(x)=2x^4+6x^311x+8


Still having problems solving this... 2x(2x + 1)^2 = 312 I started with: 2x(2x+1)(2x+1)312 = 0 2x(4x^2+4x+1)312 = 0 8x^3+8x^2+2x 312 = 0 Now what? If you don't have to solve for x, then then you have the final answer! If you have to find x: then you

"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

find all rational roots of the polynomial 6x^313x^241x12=0

Factor completely with respect to the integers. 1. 9x^2  4 2. x^3 + 64 3. 200x^2  50 4. 8x^3  64 5. x^3 + x^2 + x + 1 6. x^3  2x^2 + 4x  8 7. 2x^3 + 4x^2 + 4x + 8 8. 2x^3 + 3x^2 32x  48 9. 7x^3 + 14x^2 + 7x 10. 6x^3  18x^2  2x +6 11. 3x^4  300x^2

Find a thirddegree polynomial equation with rational coefficients that has roots 1 and i+1

How do I solve polynomial equation by finding all complex roots? The problem is: factor each expression and find all complex roots of x^3+64 I got as far as x^3+64=(x+4)(x^24x+16) Now how do i find the roots of (x+4) and the roots of (x^24x+16) Thanks

Find all positive integer values of c such that the equation x^27x+c=0 only has roots that are real and rational.

Please check my answers. Thanks! Solve the polynomial equation. In order to obtain the first root, use synthetic division to test the possible rational roots. 5.2x^313x^2+22x8=0 My answer:{1/2,2,4} 6.x^38x^2x+8=0 My answer: {1,1,8} Find the rational

Differentiate and simplify (11x)(sqrt10x5) I think you use the Product rule but square roots confuse me with it being 1/2

Two of the roots of x^4 +ax^3 +ax^2+11x+b=0 are 3 and 2. 1. Find the value of a and b 2. Find the other roots. I believe that a = 3 and b = 6. I am unsure of how to find the other roots. Please show how you found the answer.


Roots Ok, what about roots? Roots of polynomials? Square roots? Cube roots? Terminology, notation, equations using them? Help us out here a little.

Which of these rational numbers does the Rational Roots Theorem say can't be a solution to 14x7 + 13x5 − 19x4 + 7x2 − 6x − 21 = 0? A. 3/2 B. 2/7 C. 1 D. (1/2)

if f (x) is a polynomial of degree 3 whose roots are p,q,r. FIND f (3) if sum of cubes of roots is 0 and sum of squares of roots and sum of roots are unit digit of 3^2018 and 5^50666666666 respectively?

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

Use the value of the discriminant to determine the number and type of roots for the equation: (x^2+20=12x16) 1 real, irrational 2 real, rational no real 1 real, rational

Given the roots, 1/2 and 4, find: (A) The quadratic equation 2x^29x+4 ? (B) The sum of the roots 4 1/2, or 9/2 (C) The product of the roots 2 Are these answers correct?

Find all rational zeros of the function. Then (if necessary) use the depressed equation to find all roots of the equation f(x)=0 f(x)= 5x^411x^333x^2+77x14

Please check the first and help with the secondthank you Find all possible rational roots of f(x) = 2x^4  5x^3 + 8x^2 + 4x+7 1.I took the constant which is 7 and the leading coefficient which is 2 and factored them 7 factored would be 7,2 2 factored

a polynomial equation with rational coefficients has the roots 7+sgrt3, 2sgrt6 find two additional roots 7sgrt3, 2+sgrt6 3sgrt7, 6+sgrt2 7+sgrt3, 2sgrt6 3+sgrt7, 6=sgrt2 could someone help

Let h(x)=164x(x^3) Find g(96). My work: 96= 164x(x^3) (x^3)4x80=0 Using the rational roots theorm, I found that x=4 so h(4)=96, therefore g(96)=4. Find g'(96). My work: g'(96)= 1/(dh/dx at x=4) 1/((3(4)^2)4)= 1/52 Does this look ok? Also, my


The equation x^2+px+q=0, q cannot be equal to 0, has two unequal roots such that the squares of the roots are the same as the two roots. Calculate the product pq. I think the obvious root would be one but the second roots i just can't figure out!

Suppose p and q are odd integers. (a) Show that the quadratic equation x2 + px + q = 0 has no rational roots. (A number á is a “root” of that equation if: á2 + pá + q = 0. A number is rational if it is expressible as m/n for some integers m and n. )

List all possible rational roots, use synthetic division to find an actual root, then use this root to solve the equation. x^3 7x^2 +13x 7=0

The discriminant of a quadratic equation is 35. The roots are: a) unequal rational numbers b) unequal irrational numbers c) equal rational numbers d) imaginary numbers Please explain.

what are all of the possible rational roots for x to the third power x squaredx +8=0?

List the possible rational roots of the following equation x^4+3x^28x+10=0

Ax^2+bx=bx^2+a prove that it's roots are rational for all real values of a and b

Find all roots f(x) x^3+2x^215x+30 Factor f(x) completely. I can't find any roots and always get a remainder with 1, 1, 2, 2 What do you do if you cannot find a root?? Using Calc button on ti84 I got X= 5.619 Y=1.4E11 Still can't find zeros...

Show that the equation x^3+ x^23=0 has no rational roots, but that it does have an irrational root between x=1 and x=2

3x^2 kxk=3x prove that this equation has rational roots for all ration values of K thanks


What is the number of distinct possible rational roots of p(x)=2x2+7x+6? I need help on how to solve this

list all the possible rational roots of 6x42x3+5x2+x10=0

Is it possible to roughly sketch a graph(without plotting the points) from the asymptotes of a rational function? Is yes, what are the rules? For example, if I have to sketch a graph of y = (2x^2+10x12)/x^2+x6), how do I do it? I got the vertical

square roots 12a^3/25 equal what it radical and rational exponent

express the roots of unity in standard form a+bi. 1.) cube roots of unity 2.) fourth roots of unity 3.) sixth roots of unity 4.) square roots of unity

express the roots of unity in standard form a+bi. 1.) cube roots of unity 2.) fourth roots of unity 3.) sixth roots of unity 4.) square roots of unity

Prove that if p and q are rational and p is not equal to 0, the roots of the quadratic equations p x(square) + 2qx p +2q = 0.

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.

partial fraction; use the rational roots theorem to factor denominator. x^3 + 2  x^4 +8x^2 +16 i got to that and im stuck Ax+B + Cx+D   x^2 +4 x^2 + 4

I'm working with finding roots of polynomial equations with degrees of 3 or higher. I have the equation r(x)=x^46x^3+12x^2=6x13 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


I'm working with finding roots of polynomial equations with degrees of 3 or higher. I have the equation r(x)=x^46x^3+12x^2=6x13 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

use the rational zero theorem and descartes’ rule of signs to assist you in finding all real and imaginary roots for x^4+2^33x^24x+4=0

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. Anyway know of a method to use. 3x^4  8x^3  5x^2 + 16x  5

5x^210x+d=0 Determine an integer value for d such that the equation has rational, non zero roots Please show me the steps and how to answer this question :) thanks:)

relative extrema x^42x^2+5 so far I know how to find the derivative which is 4x^32x now I am stuck... Please help Huh? 4x^32x=0 2x(2x^21)=0 and what are the roots? I will give you a hint: one is x=0 The other two are in the second parenthesis. Is it

Which of the following statements correctly compares the functions of a plant's roots and stem? The stem contains a high percentage of cells that provide structural support, unlike the roots. The stem is the first part of the plant to emerge from a seed,

Does anyone know the significance of the rational zero test? Is it the rational root test? I can find the rational root test, but I don't know where I can find the reason for the rational zero test. Any clue?

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

The equation x^2+px+q=0, q cannot be equal to 0, has two unequal roots such that the squares of the roots are the same as the two roots. Calculate the product pq.

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


The equation x^2+px+q=0, q cannot be equal to 0, has two unequal roots such that the squares of the roots are the same as the two roots. Calculate the product pq.

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

I can't remember how you find the roots of quadratic equations other than determining the zeroes of the equation and finding the xintercepts. Can someone please give me a clear answer on this as my dad has been useless on this topic and I need help like

Find the result if the sumn of the roots of y= x^2+3x5 is added to the product of the roots.

if the sum of the roots and product of the roots of ax^36x2+2ax3b=0 is 3&6 respectively.Then find a and b.