How many zeros, including repeated zeros, does the function f(x)=x(x−1)(2x+4)^2 have?
4
2
3
3 answers
The function f(x) has 4 zeros.
Explain how you got that answer
To find the zeros of the function f(x), we need to solve the equation f(x) = 0.
The equation is given by x(x-1)(2x+4)^2 = 0.
First, we note that x = 0 is a solution because when x = 0, the entire expression becomes zero.
Next, we consider the factor (x - 1). The zero for the factor can be found by setting (x - 1) = 0, which gives x = 1.
Finally, we consider the factor (2x + 4)^2. The square of any real number is always positive, so in order for the factor to be zero, the term (2x + 4) must be zero.
Setting (2x + 4) = 0, we get x = -2.
Therefore, the zeros of the function f(x) = x(x-1)(2x+4)^2 are x = 0, x = 1, and x = -2.
There are three zeros in total, but x = -2 is repeated twice because of the factor (2x + 4)^2.
Therefore, the function f(x) has a total of 4 zeros, including repeated zeros.
The equation is given by x(x-1)(2x+4)^2 = 0.
First, we note that x = 0 is a solution because when x = 0, the entire expression becomes zero.
Next, we consider the factor (x - 1). The zero for the factor can be found by setting (x - 1) = 0, which gives x = 1.
Finally, we consider the factor (2x + 4)^2. The square of any real number is always positive, so in order for the factor to be zero, the term (2x + 4) must be zero.
Setting (2x + 4) = 0, we get x = -2.
Therefore, the zeros of the function f(x) = x(x-1)(2x+4)^2 are x = 0, x = 1, and x = -2.
There are three zeros in total, but x = -2 is repeated twice because of the factor (2x + 4)^2.
Therefore, the function f(x) has a total of 4 zeros, including repeated zeros.
1 answer