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

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Answer 1 · 2015-04-08T17:07:53

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,

$4 = a^2 =>a^2 = 4$

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

$c = b^2$
$=> c = 9$

What value makes c a perfect square 4x^2+12x+c4x^2+12x+c?