If {2 x^{4}-x³+3 x²-x+4}{x²-3 x+2} =f(x)+A/x-1+B/x-2 then ______

Correct Answer is : f(x)=2x2+5x+14,A+B=31f(x)=2 x²+5 x+14, A+B=31f(x)=2x2+5x+14,A+B=31

Correct Answer is : f(x)=2x2+5x+14,A+B=31f(x)=2 x²+5 x+14, A+B=31f(x)=2x2+5x+14,A+B=31

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AP EAPCET 20-Aug-2021 Shift 2 Paper

Section: Mathematics

Question : 19 of 160

Marks: +1, -0

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

=f(x)+\frac{A}{x-1}+\frac{B}{x-2}

then ______

Solution:

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

∵ Degree of numerator is greater than the degree of denominator.

∴ First we divide,

=\frac{2 x^{4}-x^{3}+3 x^{2}-x+4}{x^{2}-3 x+2} =(2 x^{2}+5 x+14)+\frac{31 x-24}{(x-2)(x-1)}

...(i)

Let

\frac{31 x-24}{(x-2(x-1)}=\frac{A}{x-1}+\frac{B}{x-2}

\Rightarrow 31-24=-A(x-2)+B(x-1)

...(ii)

Put

x=1

\Rightarrow 31-24=-A \Rightarrow A=-7

Put

x=2

in Eq. (ii)

31 \times 2-24=0+B \Rightarrow B=38

∴ From Eq. (i)

f(x)=2 x^{2}+5 x+14

and

A+B=-7+38=31

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