Find roots of polynomial $$ p(x) = 5x^4+3x^3-x^2+8 $$
Answer
The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= 0.6957+0.7572i\\[1 em]x_2 &= 0.6957-0.7572i\\[1 em]x_3 &= -0.9957+0.7224i\\[1 em]x_4 &= -0.9957-0.7224i \end{aligned} $$Explanation
Polynomial $ 5x^4+3x^3-x^2+8 $ has no rational roots that can be found using Rational Root Test, so the roots were found using quartic formulas.
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