Find all real solutions of the equation. $$x ^ { 4 } = 16 x ^ { 2 }$$
A) $x = 0 , x = 4 , x = - 4$
B) $x = 0$
C) $x = 0 , x = 16 , x = - 16$
D) $x = 0 , x = 16$
E) none of these

Question

Quizplus · Accepted Answer

First, subtract $16x^2$ from both sides to get $x^4 - 16x^2 = 0$. Factoring out $x^2$, we get $x^2(x^2 - 16) = 0$. This can be further factored into $x^2(x + 4)(x - 4) = 0$, giving us the solutions $x = 0$, $x = 4$, and $x = -4$.

Find All Real Solutions of the Equation x4=16x2x ^ { 4 } = 16 x ^ { 2 }x4=16x2

Find All Real Solutions of the Equation $x ^ { 4 } = 16 x ^ { 2 }$