Write the quadratic equation having solutions $4 i , - 4 i$
A) $x ^ { 2 } - 4 = 0$
B) $x ^ { 2 } - 16 = 0$
C) $x ^ { 2 } + 4 = 0$
D) $x ^ { 2 } + 16 = 0$
E) $x ^ { 2 } + 4 x + 16 = 0$

Question

Quizplus · Accepted Answer

The solutions given are $\pm 4i$ which means that the quadratic equation has imaginary roots. By the fundamental theorem of algebra, complex roots always occur in conjugate pairs. Hence, the factors of the quadratic equation are $(x-4i)$ and $(x+4i)$. Multiplying the factors yields:
$(x-4i)(x+4i) = x^2 - (4i)^2 = x^2 -16 $
Therefore, the correct answer is (D), $x ^ { 2 } + 16 = 0$.

Write the Quadratic Equation Having Solutions 4i,−4i4 i , - 4 i4i,−4i

Write the Quadratic Equation Having Solutions $4 i , - 4 i$