Question

find the roots of 0 = x³ - 4x² + 2x - 8. options: ±2i,4; ±√2,4; ±2,4; ±i√2,4

Explanation:

Step1: Factor by grouping

Group terms: $x^3-4x^2+2x-8 = x^2(x-4)+2(x-4)=(x^2+2)(x-4)$

Step2: Set factors to 0

Set $x-4=0$ and $x^2+2=0$

Step3: Solve for x

For $x-4=0$, $x=4$. For $x^2+2=0$, $x^2=-2 \implies x=\pm i\sqrt{2}$

Answer:

$\pm i\sqrt{2}, 4$