Find roots of polynomial $$ p(x) = b^3+15b^2+56b $$

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

$$ \begin{aligned}b_1 &= 0\\[1 em]b_2 &= -7\\[1 em]b_3 &= -8 \end{aligned} $$

Step 1:

Factor out $ \color{blue}{ b }$ from $ b^3+15b^2+56b $ and solve two separate equations:

$$ \begin{aligned} b^3+15b^2+56b & = 0\\[1 em] \color{blue}{ b }\cdot ( b^2+15b+56 ) & = 0 \\[1 em] \color{blue}{ b = 0} ~~ \text{or} ~~ b^2+15b+56 & = 0 \end{aligned} $$

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

Step 2:

The solutions of $ b^2+15b+56 = 0 $ are: $ b = -8 ~ \text{and} ~ b = -7$.

You can use step-by-step quadratic equation solver to see a detailed explanation on how to solve this quadratic equation.

Polynomial Roots Calculator