Find roots of polynomial $$ p(x) = 9x^4-30x^3+13x^2+20+4 $$
Answer
The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= 1.4418\\[1 em]x_2 &= 2.642\\[1 em]x_3 &= -0.3753+0.7478i\\[1 em]x_4 &= -0.3753-0.7478i \end{aligned} $$Explanation
Step 1:
Combine like terms:
$$ 9x^4-30x^3+13x^2+ \color{blue}{20} + \color{blue}{4} = 9x^4-30x^3+13x^2+ \color{blue}{24} $$Step 2:
Polynomial $ 9x^4-30x^3+13x^2+24 $ has no rational roots that can be found using Rational Root Test, so the roots were found using quartic formulas.
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