Asked by Stephanie Schiwietz on Jun 13, 2024

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Find a real number c such that the expression x2−14x+cx ^ { 2 } - 14 x + cx214x+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.
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Verified Answer

HJ
Hannah Jensen

Jun 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.