Question

What value makes c a perfect square `4x^2+12x+c`?

Answer 1

I may perhaps be mistaking but i think the question should be: "For what value of `c` will the expression `4x^2 + 12x + c` be a perfect square?"

In that case here's my solution:

That expression must be in the `(ax + b)^2` for it to be a perfect square, so i write

`4x^2 + 12x + c -= (ax + b)^2`

`=>`4x^2 + 12x + c-= a^2x^2 + 2abx + b^2#

Equating coefficients of the powers of `x` on both sides,

`4 = a^2 =>a^2 = 4`

`12 = 2ab =>4a^2b^2 = 144` `=> 4*4*b^2 = 144 => b^2 = 9`

`c = b^2`
`=> c = 9`