Question

List all zeros for the function f(x) = x^4 - 81. Be sure to include real and complex zeros.

Answer 1

The roots can be found as,

$\begin{gathered} x^4-81=0 \\ (x^2+9)(x^2-9)=0 \\ (x^2+9)(x+3)(x-3)=0 \\ x=\pm3i,3\&-3 \end{gathered}$

Thus, the roots of the equations are 3i,-3i,3 and -3.