Find roots of polynomial $$ p(x) = -1225x^5+320x^4+450x^3+450x^2+420x+300 $$
Answer
The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= 1.1768\\[1 em]x_2 &= 0.0933+0.698i\\[1 em]x_3 &= 0.0933-0.698i\\[1 em]x_4 &= -0.551+0.3407i\\[1 em]x_5 &= -0.551-0.3407i \end{aligned} $$Explanation
Polynomial $ -1225x^5+320x^4+450x^3+450x^2+420x+300 $ has no rational roots that can be found using Rational Root Test, so the roots were found using Newton method.
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