# trig

posted by .

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

• trig -

In the quadratic equation
ax²+bx+c=0
b/a = -(sum of the two roots)
c/a = product of the two roots.

Assume a=1, then
b=-(7-3i+7+3i)=-14
c=(7-3i)*(7+3i)=49+9=58
So the quadratic equation is
x²-14x+58=0

Check by solving the equation and you should get back 7±3i as the roots.

• trig -

x = 7 + 3i, and X = 7 - 3i.

We can use either of the 2 values of X:
X = 7 + 3i,
(X - 7) = 3i,
Square both sides:
X^2 --14X + 49 = 9(-1),
X^2 - 14X + 49 +9 = 0,
X^2 - 14X + 58 = 0.

## Respond to this Question

 First Name School Subject Your Answer

## Similar Questions

1. ### 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. ### Algebra

Find a quadratic equation with integer coefficients whose roots are 2 and7.
3. ### Math

1)Write a quadratic equation with integer coefficients that has -4+7i(Radical 3) and -4-7i(Radical 3) as its roots. 2) Solve your answer to part 1 using the quadratic formula verifying your answer
4. ### Alg2

Find a quadratic equation with integral coefficients having roots 1/2 and -5/2.
5. ### Algebra

Find the number of integer quadruples (a,b,c,d) with 0\leq a,b,c,d \leq 100, such that a and b are the roots of the quadratic equation x^2-cx+d=0, while c and d are the roots of the quadratic equation x^2-ax+b.
6. ### Algebra

Find the number of integer quadruples (a,b,c,d) with 0\leq a,b,c,d \leq 100, such that a and b are the roots of the quadratic equation x^2-cx+d=0, while c and d are the roots of the quadratic equation x^2-ax+b
7. ### Math

I can't remember how you find the roots of quadratic equations other than determining the zeroes of the equation and finding the x-intercepts. Can someone please give me a clear answer on this as my dad has been useless on this topic …
8. ### Algebra

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

if a quadratic equation with real coefficients has a discrimiant of 225, then what type of roots doe it have?
10. ### 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?

More Similar Questions