Question

what value of c makes 3x^2+24x+c contain a perfect square trinomial

Answer 1

One way to determine the value of c is to do completing the square. We do as follows:

3x^2+24x+c = 0
3x^2+24x = -c
3 (x^2 + 8x ) = -c
3 (x^2 + 8x + 16 ) = -c + 48

Since -c + 48 should be equal to zero thus,

-c + 48 = 0
c = 48