Question

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

Answer 1

Divide 15 by 2, then square the amount.

(15/2)^2 = 225/4

Answer 2

Answer:  The correct option is (D) $\dfrac{225}{4}.$

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

$y\\\\=x^2+15x+c\\\\\\=x^2+2\times x\times \dfrac{15}{2}+c\\\\\\=x^2+2\times x\times \dfrac{15}{2}+\left(\dfrac{15}{2}\right)^2+c-\left(\dfrac{15}{2}\right)^2\\\\\\=(x+\dfrac{15}{2})^2+c-\dfrac{225}{4}.$

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

$c-\dfrac{225}{4}=0\\\\\\\Rightarrow c=\dfrac{225}{4}.$

Thus, the required value of c is $\dfrac{225}{4}.$

Option (D) is correct.