Find roots of polynomial $$ p(x) = 5x^4+8x^3+15x^2+8x+6 $$
Answer
The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= -0.2352+0.7812i\\[1 em]x_2 &= -0.2352-0.7812i\\[1 em]x_3 &= -0.5648+1.2182i\\[1 em]x_4 &= -0.5648-1.2182i \end{aligned} $$Explanation
Polynomial $ 5x^4+8x^3+15x^2+8x+6 $ has no rational roots that can be found using Rational Root Test, so the roots were found using quartic formulas.
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