Find roots of polynomial $$ p(x) = x^4-x^3-46x^2+4+168 $$
Answer
The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= 1.9755\\[1 em]x_2 &= -2.0849\\[1 em]x_3 &= -5.9312\\[1 em]x_4 &= 7.0407 \end{aligned} $$Explanation
Step 1:
Combine like terms:
$$ x^4-x^3-46x^2+ \color{blue}{4} + \color{blue}{168} = x^4-x^3-46x^2+ \color{blue}{172} $$Step 2:
Polynomial $ x^4-x^3-46x^2+172 $ has no rational roots that can be found using Rational Root Test, so the roots were found using quartic formulas.
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