Find the zeros of the polynomial f(x)=5(x-5)(x+3)^2
To find the zeros of the polynomial f(x) = 5(x-5)(x+3)^2, we need to find the values of x for which f(x) = 0.
Setting f(x) = 0, we have:
5(x-5)(x+3)^2 = 0
This equation will be zero if any of the factors are equal to zero.
Setting x-5 = 0, we find x = 5 as a zero.
Setting x+3 = 0, we find x = -3 as a zero.
Setting (x+3)^2 = 0, we find (x+3) = 0. Taking the square root of both sides, we get x+3 = 0 with both positive and negative square roots. Solving for x, we find x = -3 as another zero.
Therefore, the zeros of the polynomial f(x) = 5(x-5)(x+3)^2 are x = 5 and x = -3.