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 - (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 = ((b)/(2))^2`
Using this definition for this case, we have:

`k = (((-1)/(4))/(2))^2`

`k= ( (-1)/(8) )^2`

`k = (1)/(64)`
Therefore, the perfect square trinomial is:

`x^2 - (1)/(4)x + (1)/(64)`
Answer:
The value of k is:

`k = (1)/(64)`