Question
Find roots of polynomial $$ p(x) = 15x^2-50x-x^3 $$
Answer
The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= 0\\[1 em]x_2 &= 10\\[1 em]x_3 &= 5 \end{aligned} $$Explanation
Step 1:
Write polynomial in descending order
$$ \begin{aligned} 15x^2-50x-x^3 & = 0\\[1 em] -x^3+15x^2-50x & = 0 \end{aligned} $$Step 2:
Factor out $ \color{blue}{ -x }$ from $ -x^3+15x^2-50x $ and solve two separate equations:
$$ \begin{aligned} -x^3+15x^2-50x & = 0\\[1 em] \color{blue}{ -x }\cdot ( x^2-15x+50 ) & = 0 \\[1 em] \color{blue}{ -x = 0} ~~ \text{or} ~~ x^2-15x+50 & = 0 \end{aligned} $$One solution is $ \color{blue}{ x = 0 } $. Use second equation to find the remaining roots.
Step 3:
The solutions of $ x^2-15x+50 = 0 $ are: $ x = 5 ~ \text{and} ~ x = 10$.
You can use step-by-step quadratic equation solver to see a detailed explanation on how to solve this quadratic equation.
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