ANSWER
+49/4
EXPLANATION
The given expression is
[tex] {y}^{2} - 7y[/tex]
For this to be a perfect square we must add the square of half the coefficient of y.
[tex]( { \frac{ - 7}{2} })^{2} = \frac{49}{4} [/tex]
The correct choice is the third option.
+49/4
Answer: The correct option is (C) [tex]+\dfrac{49}{4}.[/tex]
Step-by-step explanation: We are given to choose the constant term that completes the following perfect square trinomial :
[tex]T=y^2-7y.[/tex]
Let the required constant term be c.
Then, we have
[tex]y^2-7y+c\\\\\\=y^2-2\times y\times\dfrac{7}{2}+\left(\dfrac{7}{2}\right)^2+c-\left(\dfrac{7}{2}\right)^2\\\\\\=\left(y-\dfrac{7}{2}\right)^2+c-\dfrac{49}{4}.[/tex]
Therefore, to complete the perfect square trinomial, we must have
[tex]c-\dfrac{49}{4}=0\\\\\\\Rightarrow c=+\dfrac{49}{4}.[/tex]
Thus, the required constant term is [tex]+\dfrac{49}{4}.[/tex]
Option (C) is CORRECT.
