Find a real number c such that the expression $x ^ { 2 } - 14 x + c$ is a perfect square trinomial.
A) 9
B) 49
C) 59
D) 69
E) 99

Question

Quizplus · Accepted Answer

A perfect square trinomial can be factored into the square of a binomial. Specifically, $x^2-14x+c$ can be factored into $(x-7)^2+k$ for some value $k$. Expanding the right side, we have $x^2-14x+c=x^2-14x+49+k$. Thus, we must have $c=49+k$. Since $k$ can be any nonnegative number, this gives us infinitely many possible values for $c$. However, among the given choices, only $\boxed{	extbf{(B)}\ 49}$ is one of these values.

Find a Real Number C Such That the Expression x2−14x+cx ^ { 2 } - 14 x + cx2−14x+c

Find a Real Number C Such That the Expression $x ^ { 2 } - 14 x + c$