TargetIIT

[im]http://latex.codecogs.com/gif.latex?f(x)=\frac{3a}{x+a}+\frac{4b}{x+b}-\frac{5c}{x+c}-\frac{6d}{x+d} [/im] is divisible by x[p]2[/p]

the find the value of
[im] http://latex.codecogs.com/gif.latex?\frac{3}{a}+\frac{4}{b}-\frac{5}{c}-\frac{6}{d}[/im]

?

I want to add my ?. But for the question.

What does it mean divisble by x[p]2[/p]?

1.The ans is 0.

3/a+4/b-5/c-6/d=f(0).
Now as f(x)=x^2*g(x).Thus f(0)=0.

Question is wrong as f(0) should be equal to zero which is not true here.

well this is a fiitjeeaits q

maybe its wrong then [3]

i think the question shud be
f(x) = [frac]3a[p]2[/p][/]x+a[/frac] + [frac]4b[p]2[/p][/]x+b[/frac] - [frac]5c[p]2[/p][/]x+c[/frac] - [frac]6d[p]2[/p][/]x+d[/frac]
then the thing to find out will be f(0) which is equal to 0

Amritansh the question should probably have had squares in the denominator..


even then i am not convinced because probably the question meant that the numerator should have no coefficient of x and constant term...



The original question would then imply that ...

x^2 divides [im]http://codecogs.izyba.com/gif.latex?3a%28x+b%29%28x+c%29%28x+d%29+4b%28x+a%29%28x+c%29%28x+d%29-5c%28x+a%29%28x+b%29%28x+d%29-6d%28x+a%29%28x+b%29%28x+c%29[/im]
This in itself if never going to be true because this is equal to -4abcd at x=0


Otherwise as prophet sir said in the #3 the statement does not make a lot of sense...