Higher Algebra>Chapter 35 - Theory of Equations>EXAMPLES. XXXV. d.>Q 12

HARD

JEE Main

IMPORTANT

Earn 100

Remove the second term from the equation, $x^{4} + 4 x^{3} + 2 x^{2} - 4 x - 2 = 0$ .

Important Questions on Theory of Equations

HARD

JEE Main

IMPORTANT

Higher Algebra>Chapter 35 - Theory of Equations>EXAMPLES. XXXV. d.>Q 13

Remove the second term from the equation

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

.

HARD

JEE Main

IMPORTANT

Higher Algebra>Chapter 35 - Theory of Equations>EXAMPLES. XXXV. d.>Q 14

Remove the second term from the equation $x^{6} - 12 x^{5} + 3 x^{2} - 17 x + 300 = 0$ .

HARD

JEE Main

IMPORTANT

Higher Algebra>Chapter 35 - Theory of Equations>EXAMPLES. XXXV. d.>Q 15

Transform the equation

x^{3} - \frac{x}{4} - \frac{3}{4} = 0

into one, whose roots exceed by

\frac{3}{2}

the corresponding root of the given equation.

HARD

JEE Main

IMPORTANT

Higher Algebra>Chapter 35 - Theory of Equations>EXAMPLES. XXXV. d.>Q 16

Diminish by

3

, the root of the equation

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

.

MEDIUM

JEE Main

IMPORTANT

Higher Algebra>Chapter 35 - Theory of Equations>EXAMPLES. XXXV. d.>Q 18

Find the equation whose roots are the squares of the roots of

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

.

MEDIUM

JEE Main

IMPORTANT

Higher Algebra>Chapter 35 - Theory of Equations>EXAMPLES. XXXV. d.>Q 19

Find the equation whose roots are the cubes of the roots of

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

.

HARD

JEE Main

IMPORTANT

Higher Algebra>Chapter 35 - Theory of Equations>EXAMPLES. XXXV. d.>Q 20

If

a, b, c

are the roots of

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

form an equation whose roots are

k a^{- 1}, k b^{- 1}, k c^{- 1}

.

HARD

JEE Main

IMPORTANT

Higher Algebra>Chapter 35 - Theory of Equations>EXAMPLES. XXXV. d.>Q 21

If

a, b, c

are the roots of the equation

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

, form an equation whose roots are

b^{2} c^{2}, c^{2} a^{2}, a^{2} b^{2}

.