Question

which value of K will make x^2-1/4x+k a perfect square trinomial?

Answer 1

1/64, because (-1/4)/2 is -1/8, and -1/8  ^2 is 1/64

Answer 2

For this case we have the following polynomial:
 $x^2 - \frac{1}{4}x + k$
 We suppose that we have a standard equation of the form:
 $ax ^ 2 + bx + c$
 To make a perfect square trinomial, we need to complete the square.
 Therefore, the value of c is:
 $c = (\frac{b}{2})^2$
 Using this definition for this case, we have:
 $k = (\frac{\frac{-1}{4}}{2})^2$
 $k= ( \frac{-1}{8} )^2$
 $k = \frac{1}{64}$
 Therefore, the perfect square trinomial is:
 $x^2 - \frac{1}{4}x + \frac{1}{64}$
 Answer:
 The value of k is:
 $k = \frac{1}{64}$