Find roots of polynomial $$ p(x) = 4a^3+12a^2-112a $$

The roots of polynomial $ p(a) $ are:

$$ \begin{aligned}a_1 &= 0\\[1 em]a_2 &= 4\\[1 em]a_3 &= -7 \end{aligned} $$

Step 1:

Factor out $ \color{blue}{ 4a }$ from $ 4a^3+12a^2-112a $ and solve two separate equations:

$$ \begin{aligned} 4a^3+12a^2-112a & = 0\\[1 em] \color{blue}{ 4a }\cdot ( a^2+3a-28 ) & = 0 \\[1 em] \color{blue}{ 4a = 0} ~~ \text{or} ~~ a^2+3a-28 & = 0 \end{aligned} $$

One solution is $ \color{blue}{ a = 0 } $. Use second equation to find the remaining roots.

Step 2:

The solutions of $ a^2+3a-28 = 0 $ are: $ a = -7 ~ \text{and} ~ a = 4$.

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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