Find roots of polynomial $$ p(x) = 1000-500x-25x^3 $$
Answer
The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= 1.7377\\[1 em]x_2 &= -0.8688+4.7185i\\[1 em]x_3 &= -0.8688-4.7185i \end{aligned} $$Explanation
Step 1:
Write polynomial in descending order
$$ \begin{aligned} 1000-500x-25x^3 & = 0\\[1 em] -25x^3-500x+1000 & = 0 \end{aligned} $$Step 2:
Polynomial $ -25x^3-500x+1000 $ has no rational roots that can be found using Rational Root Test, so the roots were found using qubic formulas.
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