EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 2 - Quadratic Equations>JEE Main - 9th April 2017>Q 66

MEDIUM

JEE Main

IMPORTANT

Earn 100

The sum of all the real values of $x$ Satisfying the equation $2^{(x - 1) (x^{2} + 5 x - 50)} = 1$ is:

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Important Questions on Quadratic Equations

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 2 - Quadratic Equations>JEE Main - 9th April 2016>Q 67

If the equations

x^{2} + b x - 1 = 0

and

x^{2} + x + b = 0

have a common root different from

- 1,

then

|b|

is equal to :

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 2 - Quadratic Equations>JEE Main - 3rd April 2016>Q 68

The sum of all real values of

x

satisfying the equation

{(x^{2} - 5 x + 5)}^{x^{2} + 4 x - 60} = 1

is

EASY

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 2 - Quadratic Equations>JEE Main - 10th April 2016>Q 69

If

x

is a solution of the equation

\sqrt{2 x + 1} - \sqrt{2 x - 1} = 1, (x \geq \frac{1}{2})

, then

\sqrt{4 x^{2} - 1}

is equal to :

HARD

JEE Main

IMPORTANT

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

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

) :

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: