# Which of the following constants can be added to x^{2} - 10x to form a perfect square trinomial?

10, 25, 100

**Solution:**

An expression that is obtained from the square of the binomial equation is called a perfect square trinomial.

If a trinomial is in the form ax^{2} + bx + c is said to be a perfect square, if and only if it satisfies the condition b^{2} = 4ac.

A perfect square trinomial is a polynomial expression where its factors are a perfect square.

Given: x^{2} - 10x

A constant should be added to make it a perfect square trinomial.

As we know the first and middle terms, we have to find the constant that should be added at the end. We can add them by completing the square.

Middle term = -10

Dividing it by 2

= -10/2

= -5

By squaring it

= 25

x^{2} - 10x+ 25 is the required perfect square trinomial, as x^{2} - 10x+ 25 = (x-5)^{2}

Therefore, 25 should be added to make it a perfect square trinomial.

## Which of the following constants can be added to x^{2} - 10x to form a perfect square trinomial?

**Summary:**

The constant that can be added to x^{2} - 10x to form a perfect square trinomial is 25.