Question

Find the x-intercepts of the quadratic function f(x) = x² - 3x - 10.

A) x = 5 and x = -2
B) x = -2 and x = 10
C) x = 5 and x = -3
D) x = -3 and x = 2

Answer 1

The x-intercepts of the quadratic function f(x) = x² - 3x - 10 are x = 5 and x = -2.

Step-by-step explanation:

To find the x-intercepts of the quadratic function f(x) = x² - 3x - 10, we need to set f(x) equal to zero and solve for x. The equation becomes x² - 3x - 10 = 0. To solve this quadratic equation, we can use the quadratic formula: x = (-b ± √(b² - 4ac)) / (2a).

In this case, a = 1, b = -3, and c = -10. Plugging these values into the quadratic formula, we get x = (3 ± √(9 + 40)) / 2. Simplifying further, we have x = (3 ± √49) / 2, which gives x = (3 + 7) / 2 = 5 and x = (3 - 7) / 2 = -2.

Therefore, the x-intercepts of the quadratic function f(x) = x² - 3x - 10 are x = 5 and x = -2.