Which of the following constants can be added to x² - x to form a perfect square trinomial?
1/2
1/4
1

Solution:

A perfect square trinomial is of the form

(x + a)² = x² + 2a + a²

By adding a constant b

x² - x + b

It can be written as

= x² - 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 x² - x to form a perfect square trinomial.

Which of the following constants can be added to x² - x to form a perfect square trinomial?
1/2
1/4
1

Summary:

The constant that can be added to x² - x to form a perfect square trinomial is 1/4.