Find roots of polynomial $$ p(x) = x^3+x^2-21-45 $$
Answer
The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= 3.7339\\[1 em]x_2 &= -2.367+3.4747i\\[1 em]x_3 &= -2.367-3.4747i \end{aligned} $$Explanation
Step 1:
Combine like terms:
$$ x^3+x^2 \color{blue}{-21} \color{blue}{-45} = x^3+x^2 \color{blue}{-66} $$Step 2:
Polynomial $ x^3+x^2-66 $ has no rational roots that can be found using Rational Root Test, so the roots were found using qubic formulas.
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