Find roots of polynomial $$ p(x) = x^3+10x^2+41+20 $$
Answer
The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= -10.5482\\[1 em]x_2 &= 0.2741+2.3891i\\[1 em]x_3 &= 0.2741-2.3891i \end{aligned} $$Explanation
Step 1:
Combine like terms:
$$ x^3+10x^2+ \color{blue}{41} + \color{blue}{20} = x^3+10x^2+ \color{blue}{61} $$Step 2:
Polynomial $ x^3+10x^2+61 $ has no rational roots that can be found using Rational Root Test, so the roots were found using qubic formulas.
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