Intermediate Second Year Mathematics Paper 2A>Chapter 4 - Theory of Equations>Exercise 4(b)>Q I

EASY

12th Telangana Board

IMPORTANT

Earn 100

Solve $x^{3} - 3 x^{2} - 16 x + 48 = 0$ , given that the sum of two roots is zero.

Important Questions on Theory of Equations

EASY

12th Telangana Board

IMPORTANT

Intermediate Second Year Mathematics Paper 2A>Chapter 4 - Theory of Equations>Exercise 4(b)>Q I

Find the condition that

x^{3} - p x^{2} + q x - r = 0

may have the sum of two of its roots zero.

EASY

12th Telangana Board

IMPORTANT

Intermediate Second Year Mathematics Paper 2A>Chapter 4 - Theory of Equations>Exercise 4(b)>Q I

Given that the roots of

x^{3} + 3 p x^{2} + 3 q x + r = 0

are in

A . P .

. Show that

2 p^{3} - 3 q p + r = 0

.

EASY

12th Telangana Board

IMPORTANT

Intermediate Second Year Mathematics Paper 2A>Chapter 4 - Theory of Equations>Exercise 4(b)>Q I

Given that the roots of

x^{3} + 3 p x^{2} + 3 q x + r = 0

are in

G . P .

, show that

p^{3} r = q^{3}

.

EASY

12th Telangana Board

IMPORTANT

Intermediate Second Year Mathematics Paper 2A>Chapter 4 - Theory of Equations>Exercise 4(b)>Q I

If the roots of

x^{3} + 3 p x^{2} + 3 q x + r = 0

are in

H . P .

show that

2 q^{3} = r (3 p q - r)

.

EASY

12th Telangana Board

IMPORTANT

Intermediate Second Year Mathematics Paper 2A>Chapter 4 - Theory of Equations>Exercise 4(b)>Q I

Find the condition that

x^{3} - p x^{2} + q x - r = 0

may have the roots in

G . P .

EASY

12th Telangana Board

IMPORTANT

Intermediate Second Year Mathematics Paper 2A>Chapter 4 - Theory of Equations>Exercise 4(b)>Q II

Solve

9 x^{3} - 15 x^{2} + 7 x - 1 = 0

, given that two of its roots are equal.

EASY

12th Telangana Board

IMPORTANT

Intermediate Second Year Mathematics Paper 2A>Chapter 4 - Theory of Equations>Exercise 4(b)>Q II

Given that one root of

2 x^{3} + 3 x^{2} - 8 x + 3 = 0

is double the other root, find the roots of the equation.

EASY

12th Telangana Board

IMPORTANT

Intermediate Second Year Mathematics Paper 2A>Chapter 4 - Theory of Equations>Exercise 4(b)>Q II

Solve

x^{3} - 9 x^{2} + 14 x + 24 = 0

, given that two of the roots are in the ratio

3 : 2

.