what is the value of c so that x^2-11x+c is a perfect - square trinomial
To make x^2-11x+c a perfect square trinomial, we need to complete the square.
The square of the first term x^2 is x^2. To complete the square of -11x, we need to add (-11/2)^2 = 121/4.
So,
x^2 - 11x + c = (x - 11/2)^2 + c - 121/4
For this expression to be a perfect square trinomial, we need the term (x - 11/2)^2 to be the only term. Therefore,
c - 121/4 = 0
c = 121/4
So the value of c that makes x^2 - 11x + c a perfect square trinomial is c = 121/4.