EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 2 - Quadratic Equations>JEE Main - 19th April 2014>Q 73

MEDIUM

JEE Main

IMPORTANT

Earn 100

The equation $\sqrt{3 x^{2} + x + 5} = x - 3$ , where $x$ is real, has

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Important Questions on Quadratic Equations

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 2 - Quadratic Equations>JEE Main - 9th April 2014>Q 74

If

\frac{1}{\sqrt{α}}, \frac{1}{\sqrt{β}}

are the roots of the equation

a x^{2} + b x + 1 = 0, (a \neq 0, a, b \in R)

, then the equation

x (x + b^{3}) + (a^{3} - 3 a b x) = 0

has roots:

EASY

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 2 - Quadratic Equations>JEE Main - 9th April 2014>Q 75

If equations

a x^{2} + b x + c = 0, (a, b, c \in R, a \neq 0)

and

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

have a common root, then

a : b : c

equals :

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 2 - Quadratic Equations>JEE Main - 6th April 2014>Q 76

Let

α and β

be the roots of equation

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

,

p \neq 0

. If

p, q, r

are in A.P. and

\frac{1}{α} + \frac{1}{β} = 4

, then the value of

|α - β|

is

HARD

JEE Main

IMPORTANT

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

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

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 ______