Find roots of polynomial $$ p(x) = 2x^3-3x^2-11+6 $$
Answer
The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= 2.0786\\[1 em]x_2 &= -0.2893+1.0578i\\[1 em]x_3 &= -0.2893-1.0578i \end{aligned} $$Explanation
Step 1:
Combine like terms:
$$ 2x^3-3x^2 \color{blue}{-11} + \color{blue}{6} = 2x^3-3x^2 \color{blue}{-5} $$Step 2:
Polynomial $ 2x^3-3x^2-5 $ has no rational roots that can be found using Rational Root Test, so the roots were found using qubic formulas.
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