Final answer:
The zeros of the function f(x)=(x-5)²(x-4) are x = 5, with multiplicity 2, and x = 4, which is a simple zero.
Step-by-step explanation:
The zeres (zeros) of the function f(x)=(x-5)²(x-4) are found by setting the function equal to zero and solving for the values of x that satisfy the equation:
f(x) = 0 when (x-5)² = 0 or (x-4) = 0.
We can see that:
- (x-5)² = 0 when x = 5. This is a repeated zero because of the square term, which means x = 5 is a zero with multiplicity 2.
- (x-4) = 0 when x = 4. This is a simple zero.
Therefore, the zeros of the function f(x) are x = 5 and x = 4, with the zero at x = 5 being repeated.