Question

Which polynomial function has zeros when x=5,(2)/(3),-7?

Answer 1

The polynomial function with the given zeros is (x - 5)(x - 2/3)(x + 7).

Step-by-step explanation:

The polynomial function that has zeros at x = 5, 2/3, and -7 can be determined by multiplying the factors corresponding to each zero. Since x = 5 is a zero, we have (x - 5) as a factor. Similarly, (x - 2/3) and (x + 7) are the factors corresponding to x = 2/3 and x = -7, respectively. To find the polynomial function, we multiply these factors: (x - 5)(x - 2/3)(x + 7).

Answer 2

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)