Question
Find roots of polynomial $$ p(x) = x^3+2x^2-5x-6x $$
Answer
The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= 0\\[1 em]x_2 &= 2.4641\\[1 em]x_3 &= -4.4641 \end{aligned} $$Explanation
Step 1:
Combine like terms:
$$ x^3+2x^2 \color{blue}{-5x} \color{blue}{-6x} = x^3+2x^2 \color{blue}{-11x} $$Step 2:
Factor out $ \color{blue}{ x }$ from $ x^3+2x^2-11x $ and solve two separate equations:
$$ \begin{aligned} x^3+2x^2-11x & = 0\\[1 em] \color{blue}{ x }\cdot ( x^2+2x-11 ) & = 0 \\[1 em] \color{blue}{ x = 0} ~~ \text{or} ~~ x^2+2x-11 & = 0 \end{aligned} $$One solution is $ \color{blue}{ x = 0 } $. Use second equation to find the remaining roots.
Step 3:
The solutions of $ x^2+2x-11 = 0 $ are: $ x = -1-2 \sqrt{ 3 } ~ \text{and} ~ x = -1+2 \sqrt{ 3 }$.
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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