Cambridge International AS & A Level Mathematics : Pure Mathematics 2 & 3 Course Book>Chapter 1 - Algebra>END-OF-CHAPTER REVIEW EXERCISE 1>Q 18

MEDIUM

AS and A Level

IMPORTANT

Earn 100

Show that the polynomial $5 x^{3} - 13 x^{2} + 17 x - 9$ has exactly one real root.

Important Questions on Algebra

EASY

AS and A Level

IMPORTANT

Cambridge International AS & A Level Mathematics : Pure Mathematics 2 & 3 Course Book>Chapter 1 - Algebra>END-OF-CHAPTER REVIEW EXERCISE 1>Q 19

The polynomial

4 x^{3} + k x^{2} - 65 x + 18

is denoted by

f (x)

. Given that

x + 2

is a factor of

f (x)

, find the value of

k

.

HARD

AS and A Level

IMPORTANT

Cambridge International AS & A Level Mathematics : Pure Mathematics 2 & 3 Course Book>Chapter 1 - Algebra>END-OF-CHAPTER REVIEW EXERCISE 1>Q 19

The polynomial

4 x^{3} + k x^{2} - 65 x + 18

is denoted by

f (x)

. Given that

x + 2

is a factor of

f (x)

, solve the equation

f (x) = 0

.

HARD

AS and A Level

IMPORTANT

Cambridge International AS & A Level Mathematics : Pure Mathematics 2 & 3 Course Book>Chapter 1 - Algebra>END-OF-CHAPTER REVIEW EXERCISE 1>Q 19

The polynomial

4 x^{3} + k x^{2} - 65 x + 18

is denoted by

f (x)

. Given that

x + 2

is a factor of

f (x)

. Write down the roots of

f (x^{2}) = 0

MEDIUM

AS and A Level

IMPORTANT

Cambridge International AS & A Level Mathematics : Pure Mathematics 2 & 3 Course Book>Chapter 1 - Algebra>END-OF-CHAPTER REVIEW EXERCISE 1>Q 20

The polynomial

2 x^{3} - 5 x^{2} + a x + b

, where

a

and

b

are constants, is denoted by

f (x)

. It is given that when

f (x)

is divided by

x + 2

the remainder is

8

, and that when

f (x)

is divided by

x - 1

the remainder is

50

. Find the value of

a

and the value of

b

.

HARD

AS and A Level

IMPORTANT

Cambridge International AS & A Level Mathematics : Pure Mathematics 2 & 3 Course Book>Chapter 1 - Algebra>END-OF-CHAPTER REVIEW EXERCISE 1>Q 20

The polynomial

2 x^{3} - 5 x^{2} + a x + b

, where

a

and

b

are constants, is denoted by

f (x)

. It is given that when

f (x)

is divided by

x + 2

the remainder is

8

, and that when

f (x)

is divided by

x - 1

the remainder is

50

. Find the quotient and remainder when

f (x)

is divided by

x^{2} - x + 2

.

MEDIUM

AS and A Level

IMPORTANT

Cambridge International AS & A Level Mathematics : Pure Mathematics 2 & 3 Course Book>Chapter 1 - Algebra>END-OF-CHAPTER REVIEW EXERCISE 1>Q 21

The polynomial

2 x^{3} - 9 x^{2} + a x + b

, where

a

and

b

are constants, is denoted by

f (x)

. It is given that

x + 2

is a factor of

f (x)

, and that when

f (x)

is divided by

x + 1

the remainder is

30

. Find the value of

a

and the value of

b

.

HARD

AS and A Level

IMPORTANT

Cambridge International AS & A Level Mathematics : Pure Mathematics 2 & 3 Course Book>Chapter 1 - Algebra>END-OF-CHAPTER REVIEW EXERCISE 1>Q 21

The polynomial

2 x^{3} - 9 x^{2} + a x + b

, where

a

and

b

are constants, is denoted by

f (x)

. It is given that

x + 2

is a factor of

f (x)

, and that when

f (x)

is divided by

x + 1

the remainder is

30

. Solve the equation

f (x) = 0

.

MEDIUM

AS and A Level

IMPORTANT

Cambridge International AS & A Level Mathematics : Pure Mathematics 2 & 3 Course Book>Chapter 1 - Algebra>END-OF-CHAPTER REVIEW EXERCISE 1>Q 22

The polynomial

x^{3} + 3 x^{2} + 4 x + 2

is denoted by

f (x)

. Find the quotient and remainder when

f (x)

is divided by

x^{2} + x - 1

.