Answer:
x = 4 with multiplicity 2
Step-by-step explanation:
Given
f(x) = x³ - 8x² + 16x
To find the zeros equate f(x) to zero, that is
x³ - 8x² + 16x = 0 ← factor out x from each term
x(x² - 8x + 16) = 0
To factor the quadratic
Consider the factors of the constant term (+ 16) which sum to give the coefficient of the x- term (- 8)
The factors are - 4 and - 4, since
- 4 × - 4 = 16 and - 4 - 4 = - 8, hence
x² - 8x + 16) = (x - 4)(x - 4)
and
x³ - 8x² + 16x = x(x - 4)(x - 4) = 0
Equate each factor to zero and solve for x
x = 0
x- 4 = 0 ⇒ x = 4
x - 4 = 0 ⇒ x = 4
The multiple zero is x = 4 with multiplicity 2
