Which value must be added to the expression x² + x to make it a perfect square trinomial?

Solution:

A perfect square trinomial is the one, which gives specific roots value when square rooted.

Let the unknown constant value be c², that will make it a perfect square.

⇒  x² + x + c²

Comparing this to a perfect square, that is, a² + 2ab + b², we get

x = 2ab, x = a, 2b = 1, or b = 1/2

The value of b comes out to be equal to 1/2 which is also equal to c = 1/2.

And c² = 1/4.

Therefore, we need to add 1/4 to the expression x² + x to make it a perfect square.

Which value must be added to the expression x² + x to make it a perfect square trinomial?

Summary:

We need to add 1/4 to the expression x² + x to make it a perfect square.