Find roots of polynomial $$ p(x) = -13x^3+22x^2-6x-1-13 $$
Answer
The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= -0.5929\\[1 em]x_2 &= 1.1426+0.7148i\\[1 em]x_3 &= 1.1426-0.7148i \end{aligned} $$Explanation
Step 1:
Combine like terms:
$$ -13x^3+22x^2-6x \color{blue}{-1} \color{blue}{-13} = -13x^3+22x^2-6x \color{blue}{-14} $$Step 2:
Polynomial $ -13x^3+22x^2-6x-14 $ has no rational roots that can be found using Rational Root Test, so the roots were found using qubic formulas.
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