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

1/2

1/4

1

**Solution:**

A perfect square trinomial is of the form

(x + a)^{2} = x^{2} + 2a + a^{2}

By adding a constant b

x^{2} - x + b

It can be written as

= x^{2} - 2 × x × 1/2 + 1/4 + b - 1/4 [Using completing the square]

= (x - 1/2)^{2} + b - 1/4

So we get

b - 1/4 = 0

b = 1/4

Therefore, the constant 1/4 can be added to x^{2} - x to form a perfect square trinomial.

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

1/2

1/4

1

**Summary: **

The constant that can be added to x^{2} - x to form a perfect square trinomial is 1/4.

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