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AP EAMCET Engineering 21 Apr 2019 Shift 1 Paper

Section: Mathematics

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Question : 19 of 160

Marks: +1, -0

if

\frac{x^4}{(x-1)(x-2)(x-3)}

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

, then k + A - B + C =

104
52
63
$\frac{127}{2}$

Solution:

It is given that

\;\frac{x^{4}}{(x-1)(x-2)(x-3)}=x+k+\;\frac{A}{x-1}+\;\frac{B}{x-2}+\;\frac{C}{x-3}

Compare the coefficient and put

x=1

then

A=\;\frac{1}{2}

At

x=2,\;B=\;\frac{16}{-1}=-16

At

x=3,\;C=\;\frac{81}{2}

When

x=0

0=k(-1)(-2)(-3)+\;\frac{1}{2}(-2)(-3)-16(-3)(-1)+\;\frac{81}{2}(-1)(-2)

6k=3-48+81

k=6

\text{So}

k+A-B+C=6+\;\frac{1}{2}+16+\;\frac{81}{2}

=6+16+41

=63

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