Question

Which of the following constants can be added to x^2+15x to form a perfect square trinomial?

a. 15/2
b. 225/4
c. 15

Answer 1

Option C. The constant is
`(225)/(4)`

Solution:

Let us assume that the constant is c.

Now to the equation will be
`x^(2)+15 x+c`-------- (i)

We know the square formula
`(a+b)^(2)=a^(2)+2 a b+b^(2)`

As per the formula we can write the equation as,

`x^(2)+15 x+c`

`=x^(2)+2 * x *\left((15)/(2)\right)+c`

Now if we need make the equation perfect square,

Then as per the formula c should be
`\left((15)/(2)\right)^(2)=(225)/(4)`

And the equation will be the perfect square as
`\left(x+(15)/(2)\right)^(2)`

So, the constant is
`(225)/(4)`

Answer 2

Answer b.
`(225)/(4)`

Explanation:

In order to get a perfect square trinomial from a binomial of the form:
`x^2 +bx`. the term to add should be the square of half of the coeficcient "b". That is:
`((b)/(2) )^2`. Such will give you a trinomial that comes from the perfect square of the binomial:
`(x+(b)/(2))^2=x^2+bx+((b)/(2)  )^2`

In your case, b=15 therefore
`((b)/(2) )^2=((15)/(2) )^2=(225)/(4)`