# Which of the following constants can be added to x2 - 6x to form a perfect square trinomial?

6, 9, 36, None of the above

**Solution:**

A perfect square trinomial is of the form

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

Given, the equation is x^{2 }- 6x + __

Let us take the missing term as c,

now, x^{2} - 6x + c --- (2)

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

⇒ a^{2} = x^{2}

⇒ a = x

⇒ -2ab = - 6x

We know, a = x

So, -2xb = -6x

⇒ 2b = 6

⇒ b = 6/2

⇒ b = 3

⇒ b^{2} = c

⇒ c = 3^{2}

⇒ c = 9

Therefore, the constant to be added is 9.

## Which of the following constants can be added to x^{2} - 6x to form a perfect square trinomial?

**Summary:**

The constant to be added to x^{2} - 6x to form a perfect square trinomial is 9.

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