Final answer:
The quadratic equation x² - 21 = 0 has two x-intercepts, which are the solutions to the equation and can be found by taking the square root of both sides, leading to x = √21 and x = -√21.
Step-by-step explanation:
To determine the number of x-intercepts that the quadratic equation x² - 21 = 0 has, we first recognize that it is in the standard form of a quadratic equation ax² + bx + c = 0. To find the x-intercepts, we look for the values of x that make the equation equal to zero, which are the solutions to the equation. Since the equation is a perfect square trinomial, we can solve it by taking the square root of both sides. The solutions are x = √21 and x = -√21. This gives us two x-intercepts, which can be represented on a graph by the points (√21, 0) and (-√21, 0).