Find roots of polynomial $$ p(x) = x^4+4x^4-30x^2-68x-35 $$
Answer
The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= -0.7277\\[1 em]x_2 &= 3.2847\\[1 em]x_3 &= -1.2785+1.1375i\\[1 em]x_4 &= -1.2785-1.1375i \end{aligned} $$Explanation
Step 1:
Combine like terms:
$$ \color{blue}{x^4} + \color{blue}{4x^4} -30x^2-68x-35 = \color{blue}{5x^4} -30x^2-68x-35 $$Step 2:
Polynomial $ 5x^4-30x^2-68x-35 $ has no rational roots that can be found using Rational Root Test, so the roots were found using quartic formulas.
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