What are the x-intercepts of the function f(x) = -2x2 - 3x + 20?
Solution:
Given, f(x) = -2x2 - 3x + 20
x-intercept is a point on the x-axis when the curve cuts x-axis.
For polynomials x- intercept also refers to its zeros.
Consider f(x) = 0
-2x2 - 3x + 20 = 0
Multiply throughout by (-1),
2x2 + 3x - 20 = 0
2x2 + 8x - 5x - 20 = 0
2x(x + 4) - 5(x + 4) = 0
(2x - 5)(x + 4) = 0
2x - 5 = 0 ⇒ x = 5/2 = 2.5
x + 4 = 0 ⇒ x = -4
Therefore, x-intercepts are (2.5, 0) and (-4, 0).
What are the x-intercepts of the function f(x) = -2x2 - 3x + 20?
Summary:
The x-intercepts of the function f(x) = -2x2 - 3x + 20 are (2.5, 0) and (-4, 0).