Find roots of polynomial $$ p(x) = 151n-n^2-3000 $$
Answer
The roots of polynomial $ p(n) $ are:
$$ \begin{aligned}n_1 &= 127.4639\\[1 em]n_2 &= 23.5361 \end{aligned} $$Explanation
Step 1:
Write polynomial in descending order
$$ \begin{aligned} 151n-n^2-3000 & = 0\\[1 em] -n^2+151n-3000 & = 0 \end{aligned} $$Step 2:
The solutions of $ -n^2+151n-3000 = 0 $ are: $ n = \dfrac{ 151 }{ 2 }-\dfrac{\sqrt{ 10801 }}{ 2 } ~ \text{and} ~ n = \dfrac{ 151 }{ 2 }+\dfrac{\sqrt{ 10801 }}{ 2 }$.
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