# What is the value of #c# that makes #x^2-15x+c# a perfect square trinomial?

##### 2 Answers

#### Explanation:

We find:

#(x+b/2)^2 = x^2+2(x)(b/2)+(b/2)^2 = x^2+bx+b^2/4#

So in order for

#c = (b/2)^2#

In our example:

#c = (color(blue)(15)/2)^2 = 225/4#

#### Explanation:

Consider the equaton:

This equation has a single root where its discriminant

When this equation has a single root its factors will be of the form:

Hence: The trinomial will be a perfect square when the discriminant of

I.e. when

To test this result consider

Hence our trinomial is:

Which factorises to: