Find roots of polynomial $$ p(x) = 2000-1000x+45x^2-50x^3 $$
Answer
The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= 1.8407\\[1 em]x_2 &= -0.4703+4.6379i\\[1 em]x_3 &= -0.4703-4.6379i \end{aligned} $$Explanation
Step 1:
Write polynomial in descending order
$$ \begin{aligned} 2000-1000x+45x^2-50x^3 & = 0\\[1 em] -50x^3+45x^2-1000x+2000 & = 0 \end{aligned} $$Step 2:
Polynomial $ -50x^3+45x^2-1000x+2000 $ has no rational roots that can be found using Rational Root Test, so the roots were found using qubic formulas.
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