Question

The solutions to a quadratic equation are x = 2 and x = 7. If k is a nonzero constant, which of the following must be equal to the quadratic equation?. a. k(x-2)(x-7)=0. b. (x-2)(x-7)+k=0. c. (x+2)(x+7)+k=0. d. k(x+2)(x+7)=0

Answer 1

The answer is A

Explanation:

Answer 2

ANSWER


The correct option is,

`k(x - 2)(x - 7) = 0`

EXPLANATION

We were given that the solutions of the quadratic equation are

`x = 2`
and

`x = 7.`

This tells us that,


`x - 2`

and

`x - 7`

are factors of the quadratic equation.



This implies that the quadratic equation is of the form,


`(x - 2)(x - 7) = 0`

We were also told that


`k`


is a non zero constant.



This means that we can use k to multiply the whole equation and the solution will not be affected.


Our equation now becomes,


`k(x - 2)(x - 7) = 0`


Hence the correct answer is A.