Consider the rational function g(x)= 2x^ 2 +ax+5 (x-2)(x+1)(x-3)

MATHEMATICS · Multi-part · CBSE · Mathematics · Integrals · Integrals

Problem

Consider the rational function

g(x)=\frac{2x^{2}+ax+5}{(x-2)(x+1)(x-3)},

where

a

is a real parameter. (i) Write

g(x)

in the form

g(x)=\frac{A}{x-2}+\frac{B}{x+1}+\frac{C}{x-3},

expressing

A,\,B

and

C

in terms of

a

. (You need not simplify algebraic fractions at this stage.) (ii) Determine the value of

a

for which the coefficient

C

equals

0

. (iii) For the value of

a

found in part (ii), state the complete simplified decomposition of

g(x)