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#