Question

What are the x-intercepts of the quadratic function? f(x)=x^2−3x−10 Enter your answers in the boxes.

___ and ___

Answer 1

-2, 5

Explanation:

`f(x) = {x}^(2) - 3x - 10 \\ let \: f(x) = 0 \\ {x}^(2) - 3x - 10 = 0 \\ {x}^(2) - 5x + 2x - 10 = 0\\ x(x - 5) + 2(x - 5) = 0\\ (x - 5)(x + 2) = 0 \\ x - 5 = 0 \: \: or \: \: x + 2 = 0 \\ x = 5 \: \: or \: \: x = - 2 \\`

Hence, - 2 & 5 5 are the x-intercepts of the given quadratic function.