g(x)=5(x-5)(x^2-9)(x+5)^2 find all real zeros

Answer 1

To find the real zeros of the function g(x), we need to set g(x) equal to zero and solve for x.

g(x) = 5(x-5)(x^2-9)(x+5)^2 = 0

Since each factor is multiplied together, we can set each factor separately equal to zero and solve for x.

(x-5) = 0
Solving for x, we find x = 5.

(x^2-9) = 0
Factoring the quadratic, we get (x-3)(x+3) = 0
Solving for x, we find x = 3 and x = -3.

(x+5)^2 = 0
Taking the square root of both sides, we get x + 5 = 0
Solving for x, we find x = -5.

Therefore, the real zeros of the function g(x) are x = 5, x = 3, x = -3, and x = -5.