Find roots of polynomial $$ p(x) = x^4-2x^3-2x-x+1 $$
Answer
The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= 0.3157\\[1 em]x_2 &= 2.4363\\[1 em]x_3 &= -0.376+1.0765i\\[1 em]x_4 &= -0.376-1.0765i \end{aligned} $$Explanation
Step 1:
Combine like terms:
$$ x^4-2x^3 \color{blue}{-2x} \color{blue}{-x} +1 = x^4-2x^3 \color{blue}{-3x} +1 $$Step 2:
Polynomial $ x^4-2x^3-3x+1 $ has no rational roots that can be found using Rational Root Test, so the roots were found using quartic formulas.
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