Find roots of polynomial $$ p(x) = x^3+2x^3-6x^2+1 $$
Answer
The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= 0.4662\\[1 em]x_2 &= -0.3747\\[1 em]x_3 &= 1.9085 \end{aligned} $$Explanation
Step 1:
Combine like terms:
$$ \color{blue}{x^3} + \color{blue}{2x^3} -6x^2+1 = \color{blue}{3x^3} -6x^2+1 $$Step 2:
Polynomial $ 3x^3-6x^2+1 $ has no rational roots that can be found using Rational Root Test, so the roots were found using qubic formulas.
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