Find the Roots (Zeros) y=x(x-1)^3

$y = x {(x - 1)}^{3}$

Step 1

Set $x {(x - 1)}^{3}$ equal to $0$ .

$x {(x - 1)}^{3} = 0$

Step 2

Solve for $x$ .

If any individual factor on the left side of the equation is equal to $0$ , the entire expression will be equal to $0$ .

$x = 0$

${(x - 1)}^{3} = 0$

Set $x$ equal to $0$ .

$x = 0$

Set ${(x - 1)}^{3}$ equal to $0$ and solve for $x$ .

Set ${(x - 1)}^{3}$ equal to $0$ .

${(x - 1)}^{3} = 0$

Solve ${(x - 1)}^{3} = 0$ for $x$ .

Set the $x - 1$ equal to $0$ .

$x - 1 = 0$

Add $1$ to both sides of the equation.

$x = 1$

The final solution is all the values that make $x {(x - 1)}^{3} = 0$ true.

$x = 0, 1$

Step 3