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

a. 1/4B. 1/2C. 1D. 4

x²+x given, we have to make it a perfect square.

To make it a perfect square first we have to check the x term. We have to check co-efficient of x. Here only x given, that means there is 1 with it. As x means 1*x which is also x. So, co-efficient of x is 1 here.

We will have to divide co-efficient of x by 2 and have to add the square with the expression to make it a perfect square.

As co-efficient of x is 1, so 1 divided by 2 is 1/2.

We are adding the square of 1/2 with the expression.

x²+x + (1/2) ²

We know that (a+b) ² = a²+2ab+b²

So here x²+2 * (x) * (1/2) + (1/2) ² = (x+1/2) ², as 2 * (x) * (1/2) = x

So by adding (1/2) ² with it, we are getting a perfect square here.

(1/2) ² = 1/4

So, we have to add 1/4 with this expression to make it a perfect square.