Find roots of polynomial $$ p(x) = 80x^7-2030x^6 $$

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

$$ \begin{aligned}x_1 &= 0\\[1 em]x_2 &= \frac{ 203 }{ 8 } \end{aligned} $$

Step 1:

Factor out $ \color{blue}{ 10x^6 }$ from $ 80x^7-2030x^6 $ and solve two separate equations:

$$ \begin{aligned} 80x^7-2030x^6 & = 0\\[1 em] \color{blue}{ 10x^6 }\cdot ( 8x-203 ) & = 0 \\[1 em] \color{blue}{ 10x^6 = 0} ~~ \text{or} ~~ 8x-203 & = 0 \end{aligned} $$

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

Step 2:

To find the last zero, solve equation $ 8x-203 = 0 $

$$ \begin{aligned} 8x-203 & = 0 \\[1 em] 8 \cdot x & = 203 \\[1 em] x & = \frac{ 203 }{ 8 } \end{aligned} $$

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