Question

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

Answer 1

$x^2- \dfrac{1}{4} x+k$

To make the expression a perfect square, we always add $( \dfrac{b}{2} )^2$:

$k = (\dfrac{1}{4} \div 2)^2$

$k = (\dfrac{1}{4} \times \dfrac{1}{2} )^2$

$k = (\dfrac{1}{8} )^2$

$k = \dfrac{1}{64}$

Answer 2

1/64

Your square will be (x - 1/8)^2 which evaluates to x^2 - 1/4x + 1/64.