Find roots of polynomial $$ p(x) = x^4-2x^3+15x-22x+10 $$
Answer
The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= 1.225\\[1 em]x_2 &= 2.4823\\[1 em]x_3 &= -0.8536+1.6i\\[1 em]x_4 &= -0.8536-1.6i \end{aligned} $$Explanation
Step 1:
Combine like terms:
$$ x^4-2x^3+ \color{blue}{15x} \color{blue}{-22x} +10 = x^4-2x^3 \color{blue}{-7x} +10 $$Step 2:
Polynomial $ x^4-2x^3-7x+10 $ has no rational roots that can be found using Rational Root Test, so the roots were found using quartic formulas.
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