23. what is the value of c so that x^2+13x+c is a perfect square trinomial
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To determine the value of "c" so that the given expression, x^2 + 13x + c, is a perfect square trinomial, we need to follow a specific approach. A perfect square trinomial can be written in the form (a + b)^2, where "a" and "b" are constants.
In this case, the first term, x^2, suggests that "a" is equal to x. The second term, 13x, suggests that "b" is equal to (13/2)x.
To find the value of "c" that makes the trinomial a perfect square, we square the value of "b". So, (13/2)x^2 = (169/4)x^2.
Therefore, the value of "c" that makes the given expression a perfect square trinomial is (169/4).