Questions: Find all real zeros of the function. g(x)=4 x(x-9)^2(x-7)^2

Solution Steps

The function given is already factored as: \[ g(x) = 4x(x-9)^2(x-7)^2 \] To find the zeros, we need to identify the values of \(x\) that make each factor equal to zero.

Set each factor equal to zero and solve for \(x\):

1. \(4x = 0\) gives \(x = 0\).
2. \((x-9)^2 = 0\) gives \(x = 9\).
3. \((x-7)^2 = 0\) gives \(x = 7\).

The real zeros of the function are the solutions found in the previous step. Each zero is listed once, regardless of its multiplicity.

Final Answer