The solutions to a quadratic equation are x is equal to 2 and x is equal to 7 If k is a nonzero constant, which of the following must be equal to the quadratic equation?
Answer
A
open paren x minus 2 close paren times open paren x minus 7 close paren plus k is equal to 0
B
open paren x plus 2 close paren times open paren x plus 7 close paren plus k is equal to 0
C
k open paren x minus 2 close paren open paren x minus 7 close paren is equal to 0
D
k open paren x plus 2 close paren open paren x plus 7 close paren is equal to 0
Explanation
A quadratic with solutions x = 2 and x = 7 has factors (x − 2) and (x − 7), so its equation must be a nonzero constant times (x − 2)(x − 7) = 0. Choice C has exactly this form. The constant k does not change the roots because it is nonzero.
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