Find roots of polynomial $$ p(x) = z^3-16z^2+2z+2-10 $$
Answer
The roots of polynomial $ p(z) $ are:
$$ \begin{aligned}z_1 &= 15.9059\\[1 em]z_2 &= 0.0471+0.7076i\\[1 em]z_3 &= 0.0471-0.7076i \end{aligned} $$Explanation
Step 1:
Combine like terms:
$$ z^3-16z^2+2z+ \color{blue}{2} \color{blue}{-10} = z^3-16z^2+2z \color{blue}{-8} $$Step 2:
Polynomial $ z^3-16z^2+2z-8 $ has no rational roots that can be found using Rational Root Test, so the roots were found using qubic formulas.
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