Find roots of polynomial $$ p(x) = -2x^4-3x+1+3 $$
Answer
The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= 0.8986\\[1 em]x_2 &= -1.4264\\[1 em]x_3 &= 0.2639+1.2209i\\[1 em]x_4 &= 0.2639-1.2209i \end{aligned} $$Explanation
Step 1:
Combine like terms:
$$ -2x^4-3x+ \color{blue}{1} + \color{blue}{3} = -2x^4-3x+ \color{blue}{4} $$Step 2:
Polynomial $ -2x^4-3x+4 $ has no rational roots that can be found using Rational Root Test, so the roots were found using quartic formulas.
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