Find roots of polynomial $$ p(x) = -8x+2x^4-x^4-2x^3+8 $$
Answer
The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= 0.8998\\[1 em]x_2 &= 2.6934\\[1 em]x_3 &= -0.7966+1.6329i\\[1 em]x_4 &= -0.7966-1.6329i \end{aligned} $$Explanation
Step 1:
Combine like terms:
$$ -8x+ \color{blue}{2x^4} \color{blue}{-x^4} -2x^3+8 = \color{blue}{x^4} -2x^3-8x+8 $$Step 2:
Polynomial $ x^4-2x^3-8x+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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