Find roots of polynomial $$ p(x) = x^2+2x^3+6x^2+2x+5 $$
Answer
The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= -3.4213\\[1 em]x_2 &= -0.0394+0.8539i\\[1 em]x_3 &= -0.0394-0.8539i \end{aligned} $$Explanation
Step 1:
Combine like terms:
$$ \color{blue}{x^2} +2x^3+ \color{blue}{6x^2} +2x+5 = 2x^3+ \color{blue}{7x^2} +2x+5 $$Step 2:
Polynomial $ 2x^3+7x^2+2x+5 $ has no rational roots that can be found using Rational Root Test, so the roots were found using qubic formulas.
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