Find roots of polynomial $$ p(x) = x^3-5x^2-12+14 $$
Answer
The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= 0.6805\\[1 em]x_2 &= -0.5977\\[1 em]x_3 &= 4.9173 \end{aligned} $$Explanation
Step 1:
Combine like terms:
$$ x^3-5x^2 \color{blue}{-12} + \color{blue}{14} = x^3-5x^2+ \color{blue}{2} $$Step 2:
Polynomial $ x^3-5x^2+2 $ has no rational roots that can be found using Rational Root Test, so the roots were found using qubic formulas.
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