Find the values of a, b, and c for which the quadratic equation $$a x ^ { 2 } + b x + c = 0$$ has the given numbers as solutions. Then
use those values to write a quadratic equation.
-$5 + 4 \sqrt { 2 } , 5 - 4 \sqrt { 2 }$
A) $x ^ { 2 } - 10 x - 7 = 0$
B) $x ^ { 2 } + 7 x + 10 = 0$
C) $x ^ { 2 } - 5 x + 17 = 0$
D) $x ^ { 2 } - 25 x + 57 = 0$

Question

Quizplus · Accepted Answer

The sum of the roots is $(5 + 4\sqrt{2}) + (5 - 4\sqrt{2}) = 10$, and the product of the roots is $(5 + 4\sqrt{2}) \times (5 - 4\sqrt{2}) = 25 - 32 = -7$. Thus, $a = 1$, $b = -\text{sum of roots} = -10$, and $c = \text{product of roots} = -7$, leading to the equation $x^2 - 10x - 7 = 0$.

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 $a x ^ { 2 } + b x + c = 0$