Find the values of a, b, and c for which the quadratic equation $a x ^ { 2 } + b x + c = 0$ 0 has the given numbers as solutions. Then
use those values to write a quadratic equation.
-$$- 8 + 4 \sqrt { 2 } , - 8 - 4 \sqrt { 2 }$$
A) $x ^ { 2 } + 16 x + 32 = 0$
B) $x ^ { 2 } - 32 x - 16 = 0$
C) $x ^ { 2 } + 8 x + 56 = 0$
D) $x ^ { 2 } - 64 x + 96 = 0$

Question

Quizplus · Accepted Answer

Given the roots $- 8 + 4 \sqrt { 2 }$ and $- 8 - 4 \sqrt { 2 }$, the sum of the roots $S = (- 8 + 4 \sqrt { 2 }) + (- 8 - 4 \sqrt { 2 }) = -16$ and the product of the roots $P = (- 8 + 4 \sqrt { 2 }) \cdot (- 8 - 4 \sqrt { 2 }) = 64 - 32 = 32$. Using the form $x^2 - (sum \ of \ the \ roots)x + (product \ of \ the \ roots) = 0$, we get $x^2 + 16x + 32 = 0$.

Find the Values of A, B, and C for Which ax2+bx+c=0a x ^ { 2 } + b x + c = 0ax2+bx+c=0

Find the Values of A, B, and C for Which $a x ^ { 2 } + b x + c = 0$