Find roots of polynomial $$ p(x) = 8x^7-7x^8 $$

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

$$ \begin{aligned}x_1 &= 0\\[1 em]x_2 &= \frac{ 8 }{ 7 } \end{aligned} $$

Step 1:

Write polynomial in descending order

$$ \begin{aligned} 8x^7-7x^8 & = 0\\[1 em] -7x^8+8x^7 & = 0 \end{aligned} $$

Step 2:

Factor out $ \color{blue}{ -x^7 }$ from $ -7x^8+8x^7 $ and solve two separate equations:

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

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

Step 3:

To find the last zero, solve equation $ 7x-8 = 0 $

$$ \begin{aligned} 7x-8 & = 0 \\[1 em] 7 \cdot x & = 8 \\[1 em] x & = \frac{ 8 }{ 7 } \end{aligned} $$

Polynomial Roots Calculator