Asked by Stephanie Schiwietz on Jun 13, 2024
Verified
Find a real number c such that the expression x2−14x+cx ^ { 2 } - 14 x + cx2−14x+c is a perfect square trinomial.
A) 9
B) 49
C) 59
D) 69
E) 99
Perfect Square Trinomial
A trinomial expression that is the square of a binomial, characterized by having three terms where two are perfect squares and one is double the product of the square roots of those squares.
- Solve for perfect square trinomials.
Verified Answer
HJ
Hannah JensenJun 14, 2024
Final Answer :
B
Explanation :
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 $\boxed{\textbf{(B)}\ 49}$ is one of these values.
Learning Objectives
- Solve for perfect square trinomials.