what is the value of c so that x^2-11x+c is a perfect - square trinomial

Answer 1

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.