Find roots of polynomial $$ p(x) = x^3-3x^2-3+9 $$
Answer
The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= -1.1958\\[1 em]x_2 &= 2.0979+0.785i\\[1 em]x_3 &= 2.0979-0.785i \end{aligned} $$Explanation
Step 1:
Combine like terms:
$$ x^3-3x^2 \color{blue}{-3} + \color{blue}{9} = x^3-3x^2+ \color{blue}{6} $$Step 2:
Polynomial $ x^3-3x^2+6 $ has no rational roots that can be found using Rational Root Test, so the roots were found using qubic formulas.
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