Find roots of polynomial $$ p(x) = 2x^3+7x^2-28+12 $$
Answer
The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= 1.2921\\[1 em]x_2 &= -2.396+0.6713i\\[1 em]x_3 &= -2.396-0.6713i \end{aligned} $$Explanation
Step 1:
Combine like terms:
$$ 2x^3+7x^2 \color{blue}{-28} + \color{blue}{12} = 2x^3+7x^2 \color{blue}{-16} $$Step 2:
Polynomial $ 2x^3+7x^2-16 $ has no rational roots that can be found using Rational Root Test, so the roots were found using qubic formulas.
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