Question

How many zeros, including repeated zeros, does the function f(x)=x(x−1)(2x+4)^2 have?(1 point)

Answer 1

To determine the number of zeros, we need to consider the factors of the polynomial.

The function f(x)=x(x−1)(2x+4)^2 will have zeros at the values of x that make any of the factors equal to zero.

1. The factor x will be equal to zero when x=0.
2. The factor (x-1) will be equal to zero when x=1.
3. The factor (2x+4)^2 will be equal to zero when 2x+4=0. Solving for x, we get x=-2.

So, the function has three zeros: x=0, x=1, x=-2.

Therefore, the function f(x)=x(x−1)(2x+4)^2 has three zeros.