Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 2 - Theory of Equations>Exercises>Q 25

HARD

JEE Main/Advance

IMPORTANT

Earn 100

If the roots of the equation $a x^{2} - b x + c = 0$ are $α, β$ , then the roots of the equation $b^{2} c x^{2} - a b^{2} x + a^{3} = 0$ are

100% studentsanswered this correctly

Important Questions on Theory of Equations

MEDIUM

JEE Main/Advance

IMPORTANT

Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 2 - Theory of Equations>Exercises>Q 26

If

a {(p + q)}^{2} + 2 b p q + c = 0

and

a {(p + r)}^{2} + 2 b p r + c = 0; (a \neq 0)

, then

HARD

JEE Main/Advance

IMPORTANT

Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 2 - Theory of Equations>Exercises>Q 27

If

α, β

are the nonzero roots of

a x^{2} + b x + c = 0

and

α^{2}, β^{2}

are the roots of

a^{2} x^{2} + b^{2} x + c^{2} = 0

, then

a, b, c

are in

HARD

JEE Main/Advance

IMPORTANT

Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 2 - Theory of Equations>Exercises>Q 28

If the roots of the equation

a x^{2} + b x + c = 0

are of the form

\frac{(k + 1)}{k} and \frac{(k + 2)}{(k + 1)} then {(a + b + c)}^{2}

is equal to

EASY

JEE Main/Advance

IMPORTANT

Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 2 - Theory of Equations>Exercises>Q 29

If

α, β

are the nonzero roots of

a x^{2} + b x + c = 0

and

α + h, β + h

are the roots of

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

, then

h

HARD

JEE Main/Advance

IMPORTANT

Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 2 - Theory of Equations>Exercises>Q 30

If one root of

x^{2} - x - k = 0

is square of the other, then the value of

k

is

MEDIUM

JEE Main/Advance

IMPORTANT

Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 2 - Theory of Equations>Exercises>Q 31

If

α and β

be the roots of the equation

x^{2} + p x - \frac{1}{(2 p^{2})} = 0

. Where

p \in R

. Then the minimum value of

α^{4} + β^{4}

is

MEDIUM

JEE Main/Advance

IMPORTANT

Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 2 - Theory of Equations>Exercises>Q 32

If

α, β

are the roots of

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

and

γ, δ

are the roots of

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

, then

\frac{(α - γ) (α - δ)}{(β - γ) (β - δ)} =

MEDIUM

JEE Main/Advance

IMPORTANT

Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 2 - Theory of Equations>Exercises>Q 33

The value of

m

for which one of the roots of

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

is double of one of the roots of

x^{2} - x + m = 0

is