Question

Find the complex zeros of the following polynomial function.

Answer 1

Answer:

$x=\frac{-1\pm\sqrt{3}i}{2}$

Step-by-step explanation:

$f(x)=x^3-1$

$0=x^3-1$

$0=(x^2+2x+1)(x-1)$

$x-1=0$

$x=1$ <-- Real Solution

$x^2+x+1=0$

$x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$

$x=\frac{-2\pm\sqrt{2^2-4(1)(1)}}{2(1)}$

$x=\frac{-1\pm\sqrt{1^2-4(1)(1)}}{2(1)}$

$x=\frac{-1\pm\sqrt{1-4}}{2}$

$x=\frac{-1\pm\sqrt{-3}}{2}$

$x=\frac{-1\pm\sqrt{3}i}{2}$ <-- Complex Solutions