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.
-$24 \mathrm { i } , - 24 \mathrm { i }$
A) $x ^ { 2 } + 576 = 0$
B) $x ^ { 2 } + 48 + 576 = 0$
C) $x ^ { 2 } - 48 - 576 = 0$
D) $x ^ { 2 } - 576 = 0$

Question

Quizplus · Accepted Answer

The solutions $24i$ and $-24i$ are complex conjugates, so the quadratic equation can be formed by setting $x^2 - (sum\ of\ roots)x + (product\ of\ roots) = 0$. The sum of the roots $24i + (-24i) = 0$, and the product of the roots $24i \times -24i = -576i^2$. Since $i^2 = -1$, the product becomes $576$. Thus, the equation is $x^2 + 576 = 0$.

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