Find roots of polynomial $$ p(x) = 12-18x+18x^2-x^3 $$
Answer
The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= 16.9816\\[1 em]x_2 &= 0.5092+0.6689i\\[1 em]x_3 &= 0.5092-0.6689i \end{aligned} $$Explanation
Step 1:
Write polynomial in descending order
$$ \begin{aligned} 12-18x+18x^2-x^3 & = 0\\[1 em] -x^3+18x^2-18x+12 & = 0 \end{aligned} $$Step 2:
Polynomial $ -x^3+18x^2-18x+12 $ has no rational roots that can be found using Rational Root Test, so the roots were found using qubic formulas.
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