Question

find the roots of the factored polynomial, x(x - 1)^3 write your answer as a list of values separated by commas. x = submit

Explanation:

Step1: Set each factor to zero

For the polynomial \( x(x - 1)^3 \), we set each factor equal to zero. First, consider the factor \( x \). Setting \( x = 0 \) gives one root.

Step2: Solve for the other factor

Next, consider the factor \( (x - 1)^3 \). Setting \( (x - 1)^3 = 0 \), we take the cube root of both sides, which gives \( x - 1 = 0 \), so \( x = 1 \). Since the exponent is 3, the root \( x = 1 \) has multiplicity 3, but we still list it once in the set of roots (or as a single value in the list of roots for this problem's context).

Answer:

0, 1