Find the values of a, b, and c for which the quadratic equation ax2 + bx + c = 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) $x ^ { 2 } - 32 x + 16 = 0$
B) $x ^ { 2 } - 8 x + 56 = 0$
C) $x ^ { 2 } - 64 x + 96 = 0$
D) $x ^ { 2 } - 16 x + 32 = 0$

Question

Quizplus · Accepted Answer

Given the roots of the quadratic equation are $8 + 4\sqrt{2}$ and $8 - 4\sqrt{2}$, we can use the sum and product of roots formula for a quadratic equation $ax^2 + bx + c = 0$, where the sum of the roots $(-b/a)$ is $8 + 4\sqrt{2} + 8 - 4\sqrt{2} = 16$, and the product of the roots $(c/a)$ is $(8 + 4\sqrt{2})(8 - 4\sqrt{2}) = 64 - 32 = 32$. Therefore, the quadratic equation is $x^2 - 16x + 32 = 0$.

Find the Values of A, B, and C for Which 8+42,8−428 + 4 \sqrt { 2 } , 8 - 4 \sqrt { 2 }8+42​,8−42​

Find the Values of A, B, and C for Which $8 + 4 \sqrt { 2 } , 8 - 4 \sqrt { 2 }$