Find roots of polynomial $$ p(x) = x^3+5x^3-x-14 $$
Answer
The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= 1.3682\\[1 em]x_2 &= -0.6841+1.1124i\\[1 em]x_3 &= -0.6841-1.1124i \end{aligned} $$Explanation
Step 1:
Combine like terms:
$$ \color{blue}{x^3} + \color{blue}{5x^3} -x-14 = \color{blue}{6x^3} -x-14 $$Step 2:
Polynomial $ 6x^3-x-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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