Trinomials

temarie

New member
Joined
Jun 3, 2010
Messages
4
find the value of c which will make the following expression a perfect square trinomial
9x^2-24x+c

I can factor trinomials but having trouble reversing to get c
 
(ab)2 = a22ab+b2\displaystyle (a-b)^2 \ = \ a^2-2ab+b^2

9x224x+c,      a2 = 9x2      a = 3x.\displaystyle 9x^2-24x+c, \ \implies \ a^2 \ = \ 9x^2 \ \implies \ a \ = \ 3x.

24x = 2ab, 12x = ab = 3xb, b = 4, c =b2, c =16\displaystyle -24x \ = \ -2ab, \ 12x \ = \ ab \ = \ 3xb, \ b \ = \ 4, \ c \ =b^2, \ c \ =16

\(\displaystyle Check:(3x-4)^2 \ = \ 9x^2 \ -24x \ +16.\)
 
Top