Question

F(x)=x^2(x+2)(x-2)(x-5) has zeros at x=-2, x=0, x=2, and x=5

What is the sign of f on the interval -2?
A: f is always positive on the interval.

B: f is always negative on the interval.

C: f is sometimes positive and sometimes negative on the interval.
C is the answer

Answer 1

The sign of f(x) changes between each zero on the interval -2.

Step-by-step explanation:

The sign of a polynomial function is determined by the signs of its factors. In this case, the function f(x) = x^2(x+2)(x-2)(x-5) has zeros at x = -2, x = 0, x = 2, and x = 5. Therefore, the sign of f(x) changes at each of these zeros. Between -2 and 0, for example, f(x) changes from negative to positive. Similarly, between 0 and 2, f(x) changes from positive to negative, and so on. Therefore, the sign of f(x) on the interval -2 is sometimes positive and sometimes negative.

Answer 2

Answer : is C is correct