\;\;{ If }\; \;3 x²+x+1/(x-1)^4=\;a/(x-1)+\;b/(x-1)² \;+\;c/(x-1)³+\;d/(x-1)^4 \;{, }\; then {bmatrix} a & b \\ c & d {bmatrix} is equal to

Correct Answer is : [0375]{bmatrix} 0 & 3 \\ 7 & 5 {bmatrix}[0735]

{bmatrix} 3 & 7 \\ 5 & 0 {bmatrix}

{bmatrix} 0 & 3 \\ 7 & 5 {bmatrix}

{bmatrix} 0 & 7 \\ 3 & 5 {bmatrix}

{bmatrix} 3 & 5 \\ 7 & 0 {bmatrix}

Correct Answer is : [0375]{bmatrix} 0 & 3 \\ 7 & 5 {bmatrix}[0735]

Test Index

EAMCET Engineering 2010 Solved Paper

Section: Mathematics

Question : 59 of 160

Marks: +1, -0

\;\;\text{ If }\; \;\frac{3 x^2+x+1}{(x-1)^4}=\;\frac{a}{(x-1)}+\;\frac{b}{(x-1)^2}

\;+\;\frac{c}{(x-1)^3}+\;\frac{d}{(x-1)^4} \;\text{, }\;

\begin{bmatrix} a & b \\ c & d \end{bmatrix}

Solution:

\;\frac{3 x^2+x+1}{(x-1)^4}\;=\;\frac{a}{(x-1)}+\;\frac{b}{(x-1)^2}

\;+\;\frac{c}{(x-1)^3}+\;\frac{d}{(x-1)^4}

3 x^2+x+1\;=a(x-1)^3+b(x-1)^2

3 x^2+x+1\;=a (x^3-1+3 x-3 x^2)

\;+b(x-1)+d

3 x^2+x+1\;=a x^3+(-3 a+b) x^2

\;+(3 a-2 b+c) x+(-a+b-c+d)

On comparing the coefficient of like powers of

x

on both sides.

a=0,\;-3 a+b=3,3 a-2 b+c=2

\Rightarrow b=3 \Rightarrow 0-6+c=1

\Rightarrow c=7

\;\text{ and }\;\;-a+b-c+d=1

\Rightarrow 0+3-7+d=1

\Rightarrow d=5

\;\text{ Hence, }\;\;\begin{bmatrix} a & b \\ c & d \end{bmatrix}=\begin{bmatrix} 0 & 3 \\ 7 & 5 \end{bmatrix}

Go to Question:

Prev Question

Next Question