Answer:
[tex]\frac{9}{4}[/tex]
Step-by-step explanation:
Here, the given equation,
[tex]x^2 - 3x[/tex]
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,
[tex]x^2 - 3x + y = ax^2 + 2abx + b^2[/tex]
By comparing,
a = 1, 2ab = -3,
⇒ 2(1)b = -3
⇒ b = -3/2
Hence, the value of y = [tex]b^2[/tex] = [tex](-\frac{3}{2})^2[/tex] = [tex]\frac{9}{4}[/tex]
OPTION B is correct.
Using the formula for a perfect-square trinomial, it is found that [tex]\frac{9}{4}[/tex] has to be added to make it a perfect-square trinomial, hence option B is correct.
The formula for a perfect-square trinomial is given by:
[tex](a \pm b)^2 = a^2 \pm 2ab + b^2[/tex]
In this problem, the expression given is:
[tex]x^2 - 3x[/tex]
Hence, comparing to the standard formula:
[tex]a^2 = x^2 \rightarrow a = x[/tex]
[tex]2ab = -3x[/tex]
Since [tex]a = x[/tex]
[tex]2xb = -3x[/tex]
[tex]2b = -3[/tex]
[tex]b = -\frac{3}{2}[/tex]
The value that has to be added is [tex]b^2[/tex], hence:
[tex]b^2 = \left(-\frac{3}{2}\right)^2 = \frac{9}{4}[/tex]
To learn more about perfect-square trinomials, you can take a look at https://brainly.com/question/1538726
