A polynomial function that has zeros when x = 5, 2/3, -7 include the following: D. f(x) = (x - 5)(3x - 2)(x + 7).
In Mathematics and Geometry, the x-intercept refers to the zeros of any quadratic or polynomial function and it can be defined as the point where the line of a graph passes through the x-axis (x-coordinate) when the output value (y-value) is zero (0), as shown in the image attached below.
Based on the polynomial function provided below, the zeros can be calculated as follows;
f(x)=(x+5)(2x+3)(x-7)
(x + 5) = 0
x = -5 (False).
f(x)=(x+5)(3x+2)(x-7)
(3x + 2) = 0
x = -2/3 (False)
f(x)=(x-5)(2x-3)(x+7)
(2x - 3) = 0
x = 3/2 (False).
f(x)=(x-5)(3x-2)(x+7)
(x - 5) = 0
x = 5 (True).
(3x - 2) = 0
x = 2/3 (True).
(x + 7) = 0
x = - 7 (True).
Complete Question:
Which polynomial function has zeros when x=5, 2/3, -7?
A: f(x)=(x+5)(2x+3)(x-7)
B: f(x)=(x+5)(3x+2)(x-7)
C: f(x)=(x-5)(2x-3)(x+7)
D: f(x)=(x-5)(3x-2)(x+7)