Find roots of polynomial $$ p(x) = x^4-5x^3-2x+40x-48 $$
Answer
The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= 1.6733\\[1 em]x_2 &= -2.6936\\[1 em]x_3 &= 3.0101+1.2604i\\[1 em]x_4 &= 3.0101-1.2604i \end{aligned} $$Explanation
Step 1:
Combine like terms:
$$ x^4-5x^3 \color{blue}{-2x} + \color{blue}{40x} -48 = x^4-5x^3+ \color{blue}{38x} -48 $$Step 2:
Polynomial $ x^4-5x^3+38x-48 $ has no rational roots that can be found using Rational Root Test, so the roots were found using quartic formulas.
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