Quadratic Equation

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?

 

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

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

(x+2)(x+7)+k=0

k(x+2)(x+7)=0

Answer 1

Plug the values of x (x = 2 and 7) into each choice and see which choice results in a zero.  Remember that k is non-zero.  I'll do the last one for you:

 

k(x+2)(x+7) = 0

k(2+2)(7+7) = 0

k(4)(14) = 0

64k = 0

 

Since k is not equal to zero, this choice does not result in zero, so it is not the answer.  I could put x=7 into the first binomial and x = 2 into the second:

 

k(x+2)(x+7) = 0
k(7+2)(2+7) = 0
k(9)(9) = 0
81k = 0

 

Nope, that's not zero either.  So k(x+2)(x+7) is not the answer.  Try the other choices yourself; only one of them yields a zero.