Proper Way to go about Quadratic Identities (1 Viewer)

[ChrisChrisau]

Hey all,

I have this mathematics quadratic identity question and the two ways of going about it give different answers. Which is correct?

Question: 7x ^ 2 - 20x + 15 = A (x - 2)^2 + Bx(x-2) + C

Approach 1:

7x ^ 2 - 20x + 15 = Ax^2 - 4Ax + 4A + Bx^2 - 2BX + 4A + C
7x ^ 2 - 20x + 15 = (A + B)x^2 - (4A + 2B)x + 4A + C

From here, by inspection assumptions are made and we can derive 3 equations which can be simultaneously solved to give A = -17, B = 24, C= 43

Approach 2:

Instead of typing it out, I have uploaded the original at http://img17.imageshack.us/img17/2677/method2.png

Obviously, both give different answers. Which is correct?

Thanks for all help!