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

To solve $x^4 = 16x^2$, we can set the equation to 0: $x^4 - 16x^2 = 0$. Factoring out $x^2$, we get $x^2(x^2 - 16) = 0$. This further factors 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 $x ^ { 4 } = 16 x ^ { 2 }$