Find roots of polynomial $$ p(x) = x^3-11x^2+31+30 $$
Answer
The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= 2.7131\\[1 em]x_2 &= -2.1535\\[1 em]x_3 &= 10.4404 \end{aligned} $$Explanation
Step 1:
Combine like terms:
$$ x^3-11x^2+ \color{blue}{31} + \color{blue}{30} = x^3-11x^2+ \color{blue}{61} $$Step 2:
Polynomial $ x^3-11x^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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