Question

Choose the constant term that completes the perfect square trinomial.

y 2 - 7y


-49/2
+49/2
+49/4

Answer 1

Answer: The correct option is (C)
`+(49)/(4).`

Step-by-step explanation: We are given to choose the constant term that completes the following perfect square trinomial :

`T=y^2-7y.`

Let the required constant term be c.

Then, we have

`y^2-7y+c\\\\\\=y^2-2* y*(7)/(2)+\left((7)/(2)\right)^2+c-\left((7)/(2)\right)^2\\\\\\=\left(y-(7)/(2)\right)^2+c-(49)/(4).`

Therefore, to complete the perfect square trinomial, we must have

`c-(49)/(4)=0\\\\\\\Rightarrow c=+(49)/(4).`

Thus, the required constant term is
`+(49)/(4).`

Option (C) is CORRECT.

Answer 2

+49/4

Step-by-step explanation

The given expression is

`{y}^(2) - 7y`

For this to be a perfect square we must add the square of half the coefficient of y.

`( { ( - 7)/(2) })^(2) = (49)/(4)`

The correct choice is the third option.

+49/4