Question

What is the value of c so that y=x^2+15x+c is a perfect square.

A. 30
B. 15/2
C. 15/4
D. 225/4

Answer 1

divide 15 by 2, then square the amount.

(15/2)^2 = 225/4

Answer 2

Answer: The correct option is (D)
`(225)/(4).`

Step-by-step explanation: We are give to find the value of c so that the following expression becomes a perfect square.

`y=x^2+15x+c~~~~~~~~~~~~~~~~~~~(i)`

We have

`y\\\\=x^2+15x+c\\\\\\=x^2+2* x* (15)/(2)+c\\\\\\=x^2+2* x* (15)/(2)+\left((15)/(2)\right)^2+c-\left((15)/(2)\right)^2\\\\\\=(x+(15)/(2))^2+c-(225)/(4).`

So, for the given function (i) to be a perfect square, we must have

`c-(225)/(4)=0\\\\\\\Rightarrow c=(225)/(4).`

Thus, the required value of c is
`(225)/(4).`

Option (D) is correct.