PSAT Math Grid-Ins Question 123: Answer and Explanation

Question: 123

The function f(x) = (x - 3)(x + 2)((x -1)²) will intersect the x-axis how many times?

Correct Answer: 3

Explanation:

3 There are 3 values of the function where it will intersect the x-axis. You can see this by looking at the graph of the equation below:

The values of 3, -2, and 1 are all zeros of the function.

You can perhaps more easily determine the zeros of the function if you recognize that the function is already factored:

f(x) = (x - 3)(x + 2)((x - 1)²)

All you need to do is look at the values of x that would make the entire expression equal to zero. If (x - 3) = 0, if (x + 2) = 0, or if (x - 1) = 0, the entire expression is equal to zero. Since (x - 1) is squared, the (x - 1) term repeats. So you will have only three zeros even though this equation is actually to the 4th power.