Find roots of polynomial $$ p(x) = x^3-10+32x-32 $$
Answer
The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= 1.2513\\[1 em]x_2 &= -0.6256+5.7597i\\[1 em]x_3 &= -0.6256-5.7597i \end{aligned} $$Explanation
Step 1:
Combine like terms:
$$ x^3 \color{blue}{-10} +32x \color{blue}{-32} = x^3+32x \color{blue}{-42} $$Step 2:
Polynomial $ x^3+32x-42 $ has no rational roots that can be found using Rational Root Test, so the roots were found using qubic formulas.
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