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# Which of the following constants can be added to x^{2} - 3x to form a perfect square trinomial?

1 1/2, 2 1/4, 4 1/2

**Solution:**

A perfect square trinomial is of the form

(a - b)^{2} = a^{2} - 2ab + b^{2 }--- (1)

Given, the equation is x^{2 }- 3x + __

Let us take the missing term as c,

now, x^{2} - 3x + c --- (2)

Comparing (1) and (2), we get,

⇒ a^{2} = x^{2}

⇒ a = x

⇒ -2ab = - 3x

We know, a = x

So, -2xb = -3x

⇒ 2b = 3

⇒ b = 3/2

⇒ b^{2 }= c

⇒ c = (3/2)^{2}

⇒ c = 9/4

⇒ c = 2 ¼

Therefore, the constant to be added is 2 ¼

## Which of the following constants can be added to x^{2} - 3x to form a perfect square trinomial?

**Summary:**

The constant to be added to x^{2} - 3x to form a perfect square trinomial is 2 ¼.

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