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

Answer:

The answer is A

Step-by-step 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.