Find roots of polynomial $$ p(x) = 10-20x+15x^2-4x^3 $$
Answer
The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= 1.6058\\[1 em]x_2 &= 1.0721+0.6383i\\[1 em]x_3 &= 1.0721-0.6383i \end{aligned} $$Explanation
Step 1:
Write polynomial in descending order
$$ \begin{aligned} 10-20x+15x^2-4x^3 & = 0\\[1 em] -4x^3+15x^2-20x+10 & = 0 \end{aligned} $$Step 2:
Polynomial $ -4x^3+15x^2-20x+10 $ has no rational roots that can be found using Rational Root Test, so the roots were found using qubic formulas.
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