Find roots of polynomial $$ p(x) = x^4-x^3-5x^3-x-6 $$
Answer
The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= -0.9038\\[1 em]x_2 &= 6.0543\\[1 em]x_3 &= 0.4247+0.9572i\\[1 em]x_4 &= 0.4247-0.9572i \end{aligned} $$Explanation
Step 1:
Combine like terms:
$$ x^4 \color{blue}{-x^3} \color{blue}{-5x^3} -x-6 = x^4 \color{blue}{-6x^3} -x-6 $$Step 2:
Polynomial $ x^4-6x^3-x-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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