SOLUTION: Write a quadratic equation in the variable "x" having the given numbers as solutions. Type the equation in standard, ax^2 + bx + c = 0. Solution: 8, only solution I am havi

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Question 133001: Write a quadratic equation in the variable "x" having the given numbers as solutions. Type the equation in standard, ax^2 + bx + c = 0.
Solution: 8, only solution
I am having trouble backing into the equation. Can someone help explain to me.
Thank you.
Answer by solver91311(16897) About Me  (Show Source):
You can put this solution on YOUR website!
A quadratic equation ax%5E2%2Bbx%2Bc=0 has p as a root if and only if x-p is a factor of the polynomial ax%5E2%2Bbx%2Bc. Since the Fundamental Theorem of Algebra tells us that a 2nd degree equation must have 2 roots, the root 8 must have a multiplicity of 2, in other words there are two roots and they are both 8. Therefore, the factors of the polynomial must be %28x-8%29%28x-8%29.

Apply FOIL:
x%5E2-16x%2B64

And set the polynomial equal to zero:
x%5E2-16x%2B64=0