Find roots of polynomial $$ p(x) = -3x+5x^3-6x^2+2 $$
Answer
The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= 0.4297\\[1 em]x_2 &= -0.6537\\[1 em]x_3 &= 1.4241 \end{aligned} $$Explanation
Step 1:
Write polynomial in descending order
$$ \begin{aligned} -3x+5x^3-6x^2+2 & = 0\\[1 em] 5x^3-6x^2-3x+2 & = 0 \end{aligned} $$Step 2:
Polynomial $ 5x^3-6x^2-3x+2 $ has no rational roots that can be found using Rational Root Test, so the roots were found using qubic formulas.
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