Find roots of polynomial $$ p(x) = x+x^3-2x^2+1 $$
Answer
The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= -0.4656\\[1 em]x_2 &= 1.2328+0.7926i\\[1 em]x_3 &= 1.2328-0.7926i \end{aligned} $$Explanation
Step 1:
Write polynomial in descending order
$$ \begin{aligned} x+x^3-2x^2+1 & = 0\\[1 em] x^3-2x^2+x+1 & = 0 \end{aligned} $$Step 2:
Polynomial $ x^3-2x^2+x+1 $ has no rational roots that can be found using Rational Root Test, so the roots were found using qubic formulas.
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