Question

If the zeros of a quadratic function are 3 and 8, what are the factors of the function?

a) (x+8) and (x−3)
b) (x−8) and (x+3)
c) (x+8) and (x+3)
d) (x−8) and (x−3)

Answer 1

The factors of the quadratic function with zeros 3 and 8 are (x−8) and (x+3). Thus option b is correct.

Step-by-step explanation:

To find the factors of a quadratic function given its zeros, we use the relationship between the zeros and the factors. The zeros of the quadratic function are 3 and 8.

The relationship between zeros and factors of a quadratic function is expressed as (x - zero). So, for the zero 3, the factor will be (x - 3), and for the zero 8, the factor will be (x - 8).

Therefore, the factors of the quadratic function with zeros 3 and 8 are (x - 3) and (x - 8).

Option b) (x−8) and (x+3) represents these factors in the correct form. The negative sign in front of the zeros correctly corresponds to the factors of the function. Hence, option b) is the correct answer.

This method aligns with the fundamental understanding that for a quadratic equation with roots p and q, its factors are (x - p) and (x - q). Applying this rule, we determine the factors based on the given zeros. Therefore, the correct factors for the quadratic function in this case are (x - 8) and (x + 3).

Thus option b is correct.