# Which of the following constants can be added to x^{2} + x to form a perfect square trinomial?

A perfect square trinomial is an expression that can be expressed as a square of a real number.

## Answer: The constant value 1/ 2 needs to be added to x^{2} + x to make it a perfect square

Go through the steps given below, to understand the derivability of the solution.

**Explanation:**

Given expression: x^{2} + x

To find the perfect square, we need no assign a constant value to this expression, to make this of the form (a + b)^{2}.

Let the constant value added be c.

Thus, the expression becomes: x^{2} + x + c

For a perfect square of the form (a + b)^{2} , all possible terms are a^{2 }+ 2ab + b^{2}

On comparing terms of the perfect square with those of the assumed expression with constant c, we get:

a^{2} = x^{2} ⇒ a = x,

b^{2} = c

2ab = x ⇒ 2xb = x [since a = x]

dividing both the sides by 2x, we get:

b = 1/2

Therefore c = b^{2} = (1/2)^{2} = 1/4