Answer:

f(x) = - 18x -115

Step-by-step explanation:

In this problem, we are asked to find the quadratic equation having the two zeros, 23 and -5.

First solution is we multiply the factors:

x = 23; (x - 23)

x = -5; (x + 5)

f(x) = (x - 23)(x + 5)

f(x) = - 18x -115 (Final Answer)

Second solution is analyzing that quadratic equation is f(x) = a + bx + c with numerical coefficients a, b, and c. The product of the roots is equal to c/a and the sum of the roots is -b/a. Calculating:

c/a = product = 23(-5) = -115

-b/a = sum = -(23 - 5) = -18

To find the quadratic equation:

f(x) = a + bx + c

f(x) = + (-)x +

f(x) = -18x - 115 (Final Answer)