Answer: The correct option is (b) [tex]\dfrac{1}{4}.[/tex]
Step-by-step explanation: We are given to select the correct constant that can added to [tex] x^2-x[/tex], so thet it becomes a perfect square trinomial.
A perfect square trinomial is of the following form:
[tex](x+a)^2=x^2+2a+a^2.[/tex]
Let the constant to be added be 'b'. Then, we can write
[tex]x^2-x+b\\\\=x^2-2\times x\times \dfrac{1}{2}+\dfrac{1}{4}+b-\dfrac{1}{4}\\\\\\=(x-\dfrac{1}{2})^2+b-\dfrac{1}{4}.[/tex]
So, for the given expression to be perfect trinomial,
[tex]b-\dfrac{1}{4}=0\\\\\Rightarrow b=\dfrac{1}{4}.[/tex]
Thus, (b) is the correct option.
