Find roots of polynomial $$ p(x) = z^4-6z+3 $$
Answer
The roots of polynomial $ p(z) $ are:
$$ \begin{aligned}z_1 &= 0.5114\\[1 em]z_2 &= 1.6044\\[1 em]z_3 &= -1.0579+1.5928i\\[1 em]z_4 &= -1.0579-1.5928i \end{aligned} $$Explanation
Polynomial $ z^4-6z+3 $ has no rational roots that can be found using Rational Root Test, so the roots were found using quartic formulas.
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