EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 2 - Quadratic Equations>JEE Main - 10th April 2015>Q 70

HARD

JEE Main

IMPORTANT

Earn 100

If $2 + 3 i$ is one of the roots of the equation $2 x^{3} - 9 x^{2} + k x - 13 = 0, k \in R,$ then the real root of this equation (where $i^{2} = - 1$ ) :

34.62% studentsanswered this correctly

Important Questions on Quadratic Equations

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 2 - Quadratic Equations>JEE Main - 4th April 2015>Q 71

Let

α

and

β

be the roots of equation

x^{2} - 6 x - 2 = 0

. If

a_{n} = α^{n} - β^{n}, \forall n \geq 1,

then the value of

\frac{a_{10} - 2 a_{8}}{2 a_{9}}

is equal to

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 2 - Quadratic Equations>JEE Main - 11th April 2015>Q 72

If the two roots of the equation,

(a - 1) (x^{4} + x^{2} + 1) + (a + 1) {(x^{2} + x + 1)}^{2} = 0

are real and distinct, then the set of all values of

a

is equal to

MEDIUM

JEE Main

IMPORTANT

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

The equation

\sqrt{3 x^{2} + x + 5} = x - 3

, where

x

is real, has

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: