(Unknown remainder – quadratic divisor) Let be a polynomial of degree which

MATHEMATICS · Multi-part · CBSE · Mathematics · Polynomials · Polynomials

Problem

(Unknown remainder – quadratic divisor) Let

f(x)

be a polynomial of degree

4

which, on division by

g(x)=x^{2}+3x-1

, leaves quotient

q(x)=x^{2}-2x+4

and remainder

r(x)=ax+b

, where

a

and

b

are real numbers. Further, it is given that

f(1)=10

and

f(-3)=20

. (i) Express

f(x)

in terms of

a

and

b

. (ii) Using the given values of

f(1)

and

f(-3)

, obtain two equations in

a

and

b

and hence determine their values. (iii) Write the complete expression for

f(x)

and find the value of

f(-1)