To find the number of zeros for the function, we need to determine the number of times the function crosses the x-axis or "hits" zero.
The function f(x) = x(x - 1)(2x + 4)^2 will have zeros at three different values of x:
1. When x = 0 (from the factor x)
2. When x = 1 (from the factor x - 1)
3. When (2x + 4)^2 = 0
Simplifying, we have:
(2x + 4)^2 = 0
2x + 4 = 0 or -2x - 4 = 0
2x = -4 or -2x = 4
x = -2 or x = -2
So, the function has a repeated zero at x = -2 and zeros at x = 0 and x = 1.
Therefore, the function f(x) = x(x - 1)(2x + 4)^2 has 3 zeros. Answer: \boxed{3}.
How many zeros, including repeated zeros, does the function f(x)=x(x−1)(2x+4)^2 have?(1 point)
The degree cannot be determined from the information provided.
4
3
2
1 answer
1 answer