coefficient of x^2 and x?

Question

This is taken from my text book.
In my my text book:
A(x^2+1)+(Bx+C)x= (A+B)x^2+Cx+A
then it is written:The coefficient of x^2 ,"A+B=0",and coefficient of x,"C=0".
But i don't understand Why "A+B=0" and "C=0"
Give answer with explaination.

Answer 1

Distribute what you've got, combine like terms, and it will be easier to see.

A(x² + 1) + (Bx + C)x
= Ax² + A + Bx² + Cx
= (A + B)x² + Cx + A

As to why (A + B) must equal zero or why C must equal zero would depend on the rest of your problem. You started with

A(x² + 1) + (Bx + C)x = (A + B)x² + Cx + A, then showed that the left side simplifies to the same as the right.
A(x² + 1) + (Bx + C)x = (A + B)x² + Cx + A
(A + B)x² + Cx + A = (A + B)x² + Cx + A

By solving for x, you can subtract the x² and x terms from both sides, leaving
0x² + 0x + A = 0x² + 0x + A, or A = A.
For the equation to hold true, the x² coefficient (A + B) must equal 0 (because it drops out of the equation), and the x coefficient (C) must also equal 0 (for the same reason).

Since the final solution for x leads to A = A, A can be any number... but for the original equation to hold true, C must be 0, and B has to be the additive inverse (opposite) of A.

Answer 2

I don't entirely understand the question. But if you expand all the terms on each side, you get:
Ax^2 + A + Bx^2 + Cx = Ax^2 + Bx^2 +Cx + A, which is tautological: it is true for all A, B, C, and x. You cannot conclude from this that A + B = 0, nor that C = 0.

Answer 3

My guess is that you are doing partial fraction decompositions and that this polynomial is being set equal to something/ In that case, you equate coefficients between this polynomial and whatever other polynomial you have. By the nature of what you wrote, it seems that the other polynomial is just a constant, so the x^2 and x coefficients are zero. Since I don't know which constant, I can't say what A will be, but it will be that constant.

Answer 4

it is x^2(A+B)+A+Cx=x^2(A+B)+A+Cx
now without loss of generality we can say to satisfy the eq. A+B=0,C=0

Answer 5

Instead of giving the question, you have given the solution given in your book.

Ask the question, and you can get an answer. As to why A+B=0, dependson whatthe question says.

Answer 6

if (A+B)x^2 + Cx + A = 0 then the answer is:
x = (-C +/- SQRT( C^2 - 4(A+B)A) )/2(A+B)
clearly your book is f***ed