Find roots of polynomial $$ p(x) = x^4-10x+5x^2+100x+100 $$
Answer
The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= -1.218\\[1 em]x_2 &= -3.531\\[1 em]x_3 &= 2.3745+4.1969i\\[1 em]x_4 &= 2.3745-4.1969i \end{aligned} $$Explanation
Step 1:
Combine like terms:
$$ x^4 \color{blue}{-10x} +5x^2+ \color{blue}{100x} +100 = x^4+5x^2+ \color{blue}{90x} +100 $$Step 2:
Polynomial $ x^4+5x^2+90x+100 $ has no rational roots that can be found using Rational Root Test, so the roots were found using quartic formulas.
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