Higher Algebra>Chapter 35 - Theory of Equations>EXAMPLES. XXXV. d.>Q 1

EASY

JEE Main

IMPORTANT

Earn 100

Transform the equation $x^{3} - 4 x^{2} + \frac{1}{4} x - \frac{1}{9} = 0$ into another with integral coefficients, and unity for the coefficient of the first term.

Important Questions on Theory of Equations

MEDIUM

JEE Main

IMPORTANT

Higher Algebra>Chapter 35 - Theory of Equations>EXAMPLES. XXXV. d.>Q 2

Transform the equation

3 x^{4} - 5 x^{3} + x^{2} - x + 1 = 0

into another, the coefficients of whose first term is unity.

HARD

JEE Main

IMPORTANT

Higher Algebra>Chapter 35 - Theory of Equations>EXAMPLES. XXXV. d.>Q 3

Solve the equation

2 x^{4} + x^{3} - 6 x^{2} + x + 2 = 0

.

HARD

JEE Main

IMPORTANT

Higher Algebra>Chapter 35 - Theory of Equations>EXAMPLES. XXXV. d.>Q 4

Solve the equation

x^{4} - 10 x^{3} + 26 x^{2} - 10 x + 1 = 0

.

HARD

JEE Main

IMPORTANT

Higher Algebra>Chapter 35 - Theory of Equations>EXAMPLES. XXXV. d.>Q 5

Solve the equation

x^{5} - 5 x^{4} + 9 x^{3} - 9 x^{2} + 5 x - 1 = 0

.

HARD

JEE Main

IMPORTANT

Higher Algebra>Chapter 35 - Theory of Equations>EXAMPLES. XXXV. d.>Q 6

Solve the equation

4 x^{6} - 24 x^{5} + 57 x^{4} - 73 x^{3} + 57 x^{2} - 24 x + 4 = 0

.

HARD

JEE Main

IMPORTANT

Higher Algebra>Chapter 35 - Theory of Equations>EXAMPLES. XXXV. d.>Q 7

Solve the equation

3 x^{3} - 22 x^{2} + 48 x - 32 = 0

, the roots of which are in harmonic progression.

HARD

JEE Main

IMPORTANT

Higher Algebra>Chapter 35 - Theory of Equations>EXAMPLES. XXXV. d.>Q 8

The roots of $x^{3} - 11 x^{2} + 36 x - 36 = 0$ are in harmonic progression, find them.

HARD

JEE Main

IMPORTANT

Higher Algebra>Chapter 35 - Theory of Equations>EXAMPLES. XXXV. d.>Q 9

If the roots of the equation

x^{3} - a x^{2} + x - b = 0

are in harmonic progression, show that the mean root is

3 b

.