Find roots of polynomial $$ p(x) = x^4-x^3+7 $$
Answer
The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= 1.4398+1.0963i\\[1 em]x_2 &= 1.4398-1.0963i\\[1 em]x_3 &= -0.9398+1.12i\\[1 em]x_4 &= -0.9398-1.12i \end{aligned} $$Explanation
Polynomial $ x^4-x^3+7 $ has no rational roots that can be found using Rational Root Test, so the roots were found using quartic formulas.
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