Question

Which value must be added to the expression x^2-3x to make it a perfect-square trinomial?

Answer 1

Answer:

You must add 9/4 in order to make this a perfect square.

Step-by-step explanation:

To make any binomial into a perfect square trinomial, you have to take the middle term (-3), cut it in half (-3/2) and then square it (9/4). This will give you the constant to make a perfect square trinomial every time.

Answer 2

Answer:

$\frac{9}{4}$

Step-by-step explanation:

Here, the given equation,

$x^2 - 3x$

Let y be the the value after adding the given equation will convert to a perfect square trinomial,

Also, a perfect square trinomial can be written as ( ax + b )² or ax² + 2abx+ b²,

That is,

$x^2 - 3x + y = ax^2 + 2abx + b^2$

By comparing,

a = 1, 2ab = -3,

⇒ 2(1)b = -3

⇒ b = -3/2

Hence, the value of y = $b^2$ = $(-\frac{3}{2})^2$ = $\frac{9}{4}$

OPTION B is correct.