ANSWER
[tex]2 \frac{1}{4} [/tex]
EXPLANATION
We want to find the constant that must be added to
[tex] {x}^{2} - 3x[/tex]
to form a perfect square.
Comparing the given expression to
[tex] a{x}^{2} + bx + c[/tex]
we have
a=1 , b=-3 , and c=0.
We need to add
[tex] {( \frac{b}{2a} })^{2} [/tex]
We substitute the values to get,
[tex]{( \frac{ - 3}{2(1)} })^{2} = \frac{9}{4} [/tex]
We change this to mix numbers to get,
[tex]2 \frac{1}{4} [/tex]
The last choice is correct.
