Digital PSAT Math Practice Question 192: Answer and Explanation

Question: 192

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, which we can see 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:

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, or (x + 2) = 0, or (x - 1) = 0, the entire expression is equal to zero. Also, since (x - 1) is squared, the (x - 1) term repeats, so we will have only three zeros even though this will end up being a quartic equation (to the fourth power).