Question

What value of c makes x2-24x+c a perfect square trinomial?

Answer 1

144

Explanation:

Perfect square formula: a^2 - 2ab + b^2 (because that equals (a-b)^2)

x^2-2*12x+c

a = 1

b = 12

12^2 = 144

Answer 2

The value of
`c =144` makes
`x^(2)-24x+c` perfect square.

Explanation:

We have to make
`x^(2)-24x+c`

Since, Perfect square formula:
`a^(2) - 2ab + b^(2)=(a-b)^(2)`

Re-write
`x^(2)-24x+c` as,

`x^(2)-2* 12x+c`

Compare above with
`a^(2) - 2ab + b^(2)`

Where a = x and b= 12

so,
`b=12`

⇒
`c =12^(2)=144`

Hence,
`(a-b)^(2)=(x-12)^(2)`

Therefore, the value of
`c =144` makes
`x^(2)-24x+c` perfect square.