Final answer:
The zeros of the function y = (x-5)(x + 2)^2 are x = 5 and x = -2, with x = -2 being a zero of multiplicity 2.
Step-by-step explanation:
To find the zeros of the function y = (x-5)(x + 2)^2, you need to set the function equal to zero and solve for x. The solutions to the equation are the zeros of the function.
The given function has two factors: (x-5) and (x + 2)^2. For the function to be zero, either (x-5) must be zero, or (x + 2)^2 must be zero. Solving for x in each case gives us:
- x - 5 = 0 → x = 5
- (x + 2)^2 = 0 → x + 2 = 0 (taking the square root of both sides) → x = -2
Since (x + 2)^2 is squared, the zero at x = -2 has a multiplicity of 2, which means it is a repeated zero. Therefore, the zeros of the function are x = 5 and x = -2, with x = -2 being a double zero.