Consider the polynomial

MATHEMATICS · Subjective · CBSE · Mathematics · Polynomials · Polynomials

Problem

g(x)=x^{4}+px^{3}+qx^{2}+rx-20

. (i) It is given that

x=2

is a zero of

g(x)

. Write the corresponding condition on

p, q,

and

r

. (ii) It is also given that

x=-4

is a zero of

g(x)

. Write the second condition on

p, q,

and

r

. (iii) When

g(x)

is divided by

(x-1)

, the remainder is

10

. Write the third condition on

p, q,

and

r

. (iv) Solve the simultaneous equations obtained in parts (i)–(iii) to find the values of

p, q,

and

r