Let , where , and are non-zero integers. (i) Show that is a common factor of . (ii)…

MATHEMATICS · Subjective · CBSE · Mathematics · Polynomials · Polynomials

Problem

Let

q(x)=ax^{4}+bx^{3}+cx^{2}

, where

a

b

and

c

are non-zero integers. (i) Show that

x^{2}

is a common factor of

q(x)

. (ii) Prove that

x^{2}

is the greatest common factor of

q(x)

if and only if

a

b

and

c

have no common factor other than

1

. (iii) Suppose now that

a=8

b=12

and

c=20

. Find the GCF of the coefficients, and then factorise

q(x)

completely. (iv) Using the factorised form from part (iii), solve

q(x)=0