Question

Find the zeros of each functoin y = (x-5)(x 2)^2

Answer 1

The zeros of the function y = (x-5)(x-2)^2 are x = 5 and x = 2. The zero at x = 2 is a double root because it has multiplicity 2.

Step-by-step explanation:

The student has asked to find the zeros of the function y = (x-5)(x-2)^2. To find the zeros of the function, we need to set the function equal to zero and solve for x. The given function is already factored, which simplifies the process.

Setting y to zero gives:

• 0 = (x-5)(x-2)^2

This equation indicates that the function can be zero if either (x-5) = 0 or (x-2)^2 = 0.

Solving for x when (x-5) = 0:

• x = 5

This gives us one zero at x = 5. Now let's solve for x when (x-2)^2 = 0:

• (x-2)(x-2) = 0
• x - 2 = 0
• x = 2

This gives us a repeated zero since (x-2) is squared, meaning that x = 2 is a zero with multiplicity 2.

Thus, the function has zeros at x = 5 and x = 2, with the zero at x = 2 being a double root.