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.
-$5 , - 8$
A) $x ^ { 2 } + 3 x - 40 = 0$
B) $x ^ { 2 } - 40 x + 3 = 0$
C) $x ^ { 2 } - 3 x - 40 = 0$
D) $x ^ { 2 } - 40 x - 3 = 0$

Question

Quizplus · Accepted Answer

Given the roots $5$ and $-8$, the sum of the roots is $5 + (-8) = -3$ and the product of the roots is $5 \times -8 = -40$. According to Vieta's formulas, for a quadratic equation $ax^2 + bx + c = 0$, the sum of the roots is $-b/a$ and the product of the roots is $c/a$. Assuming $a = 1$, we get $b = -3$ and $c = -40$, leading to the equation $x^2 + 3x - 40 = 0$.

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