Test Index

TS EAMCET 4 May 2018 Shift 1 Solved Paper

Section: Mathematics

© examsnet.com

Question : 19 of 160

Marks: +1, -0

if

\frac{x^4+x^3+2x^2-2x+1}{x^3+x^2}

\frac{A}{x}+\frac{B}{x^2}+\frac{C}{x+1}

then A + B + C =

P (0)
P (2)
P (3)
P (4)

Solution:

Consider the expression.

\frac{x^{4}+x^{3}+2x^{2}-2x+1}{x^{3}+x^{2}}

=P(x)+\frac{A}{x}+\frac{B}{x^{2}}+\frac{C}{x+1}

Let

P(x)=x

The above expression can now be simplified as,

\frac{x^{4}+x^{3}+2x^{2}-2x+1}{x^{3}+x^{2}}=x+\frac{A}{x}

+\frac{B}{x^{2}}+\frac{C}{x+1}

x+\frac{2x^{2}-2x+1}{x^{3}+x^{2}}=x+\frac{A}{x}+\frac{B}{x^{2}}+\frac{C}{x+1}

\frac{2x^{2}-2x+1}{x^{3}+x^{2}}

=\frac{A(x)(x+1)+B(x+1)+Cx^{2}}{x^{3}+x^{2}}

2x^{2}-2x+1=A(x)(x+1)

+B(x+1)+Cx^{2}

Compare the coefficient of like terms,

A+C=2

……. (I)

A+B=-2

……. (II)

And,

B=1

……. (III)

Therefore,

A=-3

B=1

C=5

Hence,

A+B+C=3

And

P(x)=x

Therefore,

A+B+C=P(3)

© examsnet.com

Go to Question:

Prev Question

Next Question