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

Question

05-07-2016
Mathematics

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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

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kudzordzifrancis kudzordzifrancis · Answer 1 · 2018-11-14T05:57:47+01:00

ANSWER

The correct option is,
[tex]k(x - 2)(x - 7) = 0[/tex]

EXPLANATION

We were given that the solutions of the quadratic equation are
[tex]x = 2[/tex]
and
[tex]x = 7.[/tex]

This tells us that,

[tex]x - 2[/tex]

and
[tex]x - 7[/tex]

are factors of the quadratic equation.

This implies that the quadratic equation is of the form,

[tex](x - 2)(x - 7) = 0[/tex]

We were also told that

[tex]k[/tex]

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,

[tex]k(x - 2)(x - 7) = 0[/tex]

Hence the correct answer is A.

reillyfifes reillyfifes · Answer 2 · 2018-12-06T02:02:14+01:00

reillyfifes reillyfifes

06-12-2018

Answer:

The answer is A

Step-by-step explanation:

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