Question

The function y = (x² - 1)(x² - 2) has how many x-intercepts?

a) 2
b) 3
c) 4
d) 0

Answer 1

The function y = (x² - 1)(x² - 2) has four x-intercepts, which are the solutions to the two separate equations x² - 1 = 0 and x² - 2 = 0. The x-intercepts are at x = -1, 1, -√2, and √2.

Step-by-step explanation:

The function given is y = (x² - 1)(x² - 2). To find the number of x-intercepts, we need to determine for which values of x the function equals zero. The x-intercepts are the solutions to the equation x² - 1 = 0 and x² - 2 = 0.

Solving x² - 1 = 0, we get x = ±1. Solving x² - 2 = 0, we get x = ±√2.

Therefore, there are four x-intercepts at x = -1, 1, -√2, and √2, which corresponds to option (c) 4.