Find roots of polynomial $$ p(x) = 118709x+10031x^2 $$

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

$$ \begin{aligned}x_1 &= 0\\[1 em]x_2 &= -\frac{ 118709 }{ 10031 } \end{aligned} $$

Step 1:

Write polynomial in descending order

$$ \begin{aligned} 118709x+10031x^2 & = 0\\[1 em] 10031x^2+118709x & = 0 \end{aligned} $$

Step 2:

Factor out $ \color{blue}{ x }$ from $ 10031x^2+118709x $ and solve two separate equations:

$$ \begin{aligned} 10031x^2+118709x & = 0\\[1 em] \color{blue}{ x }\cdot ( 10031x+118709 ) & = 0 \\[1 em] \color{blue}{ x = 0} ~~ \text{or} ~~ 10031x+118709 & = 0 \end{aligned} $$

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

Step 3:

To find the second zero, solve equation $ 10031x+118709 = 0 $

$$ \begin{aligned} 10031x+118709 & = 0 \\[1 em] 10031 \cdot x & = -118709 \\[1 em] x & = - \frac{ 118709 }{ 10031 } \end{aligned} $$

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