Find roots of polynomial $$ p(x) = x^4-14x^3+71x^2-154+120 $$
Answer
The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= 0.7459\\[1 em]x_2 &= -0.6498\\[1 em]x_3 &= 6.952+4.6711i\\[1 em]x_4 &= 6.952-4.6711i \end{aligned} $$Explanation
Step 1:
Combine like terms:
$$ x^4-14x^3+71x^2 \color{blue}{-154} + \color{blue}{120} = x^4-14x^3+71x^2 \color{blue}{-34} $$Step 2:
Polynomial $ x^4-14x^3+71x^2-34 $ has no rational roots that can be found using Rational Root Test, so the roots were found using quartic formulas.
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