Find roots of polynomial $$ p(x) = -2x^4-3x+x^2+3 $$
Answer
The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= -1.4817\\[1 em]x_2 &= 0.8702\\[1 em]x_3 &= 0.3058+1.0343i\\[1 em]x_4 &= 0.3058-1.0343i \end{aligned} $$Explanation
Step 1:
Write polynomial in descending order
$$ \begin{aligned} -2x^4-3x+x^2+3 & = 0\\[1 em] -2x^4+x^2-3x+3 & = 0 \end{aligned} $$Step 2:
Polynomial $ -2x^4+x^2-3x+3 $ has no rational roots that can be found using Rational Root Test, so the roots were found using quartic formulas.
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