EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 2 - Quadratic Equations>JEE Main - 7th April 2013>Q 77

HARD

JEE Main

IMPORTANT

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The real number $k$ for which the equation, $2 x^{3} + 3 x + k = 0$ has two distinct real roots in $[0, 1]$ belongs to

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Important Questions on Quadratic Equations

EASY

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 2 - Quadratic Equations>JEE Main - 7th April 2013>Q 78

If the equations

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

and

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

a, b, c \in R,

have a common root, then

a : b : c

is:

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 2 - Quadratic Equations>JEE Main - 24 June 2022 Shift 1>Q 79

If the sum of the squares of the reciprocals of the roots

α

and

β

of the equation

3 x^{2} + λ x - 1 = 0

is

15

, then

6 {(α^{3} + β^{3})}^{2}

is equal to

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 2 - Quadratic Equations>JEE Main - 24 June 2022 Shift 2>Q 80

The sum of all real roots of equation

(e^{2 x} - 4) (6 e^{2 x} - 5 e^{x} + 1) = 0

is

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 2 - Quadratic Equations>JEE Main - 25 June 2022 Shift 1>Q 81

For a natural number

n

, let

α_{n} = 19^{n} - 12^{n}

. Then, the value of

\frac{31 α_{9} - α_{10}}{57 α_{8}}

is ______

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 2 - Quadratic Equations>JEE Main - 25 June 2022 Shift 2>Q 82

Let

a, b \in R

be such that the equation

a x^{2} - 2 b x + 15 = 0

has repeated root

α

and if

α

and

β

are the roots of the equation

x^{2} - 2 b x + 21 = 0

, then

α^{2} + β^{2}

is equal to:

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 2 - Quadratic Equations>JEE Main - 26 June 2022 Shift 2>Q 83

If

p

and

q

are real number such that

p + q = 3, p^{4} + q^{4} = 369

, then the value of

{(\frac{1}{p} + \frac{1}{q})}^{- 2}

is equal to

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 2 - Quadratic Equations>JEE Main - 26 June 2022 Shift 1>Q 84

The sum of the cubes of all the roots of the equation

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

is _____.

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 2 - Quadratic Equations>JEE Main - 27 June 2022 Shift 1>Q 85

If the sum of all the roots of the equation

e^{2 x} - 11 e^{x} - 45 e^{- x} + \frac{81}{2} = 0

is

\log_{e} P

, then

P

is equal to _____.