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.
-$4 i , - 4 i$
A) $x ^ { 2 } - 8 - 16 = 0$
B) $x ^ { 2 } - 16 = 0$
C) $x ^ { 2 } + 8 + 16 = 0$
D) $x ^ { 2 } + 16 = 0$

Question

Quizplus · Accepted Answer

The solutions to a quadratic equation are given by the formula $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$. For complex solutions $4i$ and $-4i$, the sum of the solutions ($4i - 4i$) is 0, which means $b = 0$. The product of the solutions ($4i \cdot -4i$) is $-16i^2$, and since $i^2 = -1$, the product is 16. This corresponds to $c/a$, and since $a = 1$ for the quadratic equation in standard form $x^2 + bx + c = 0$, $c = 16$. Therefore, the correct equation is $x^2 + 16 = 0$.

Find the Values of A, B, and C for Which 4i,−4i4 i , - 4 i4i,−4i

Find the Values of A, B, and C for Which $4 i , - 4 i$