Find roots of polynomial $$ p(x) = x^4-x^3-29x-x-30 $$
Answer
The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= -0.9452\\[1 em]x_2 &= 3.7317\\[1 em]x_3 &= -0.8932+2.7762i\\[1 em]x_4 &= -0.8932-2.7762i \end{aligned} $$Explanation
Step 1:
Combine like terms:
$$ x^4-x^3 \color{blue}{-29x} \color{blue}{-x} -30 = x^4-x^3 \color{blue}{-30x} -30 $$Step 2:
Polynomial $ x^4-x^3-30x-30 $ has no rational roots that can be found using Rational Root Test, so the roots were found using quartic formulas.
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