Find roots of polynomial $$ p(x) = x^3+3x^3+50x^2+x+1000000 $$
Answer
The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= -67.449\\[1 em]x_2 &= 27.4745+54.3292i\\[1 em]x_3 &= 27.4745-54.3292i \end{aligned} $$Explanation
Step 1:
Combine like terms:
$$ \color{blue}{x^3} + \color{blue}{3x^3} +50x^2+x+1000000 = \color{blue}{4x^3} +50x^2+x+1000000 $$Step 2:
Polynomial $ 4x^3+50x^2+x+1000000 $ has no rational roots that can be found using Rational Root Test, so the roots were found using qubic formulas.
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