EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 2 - Quadratic Equations>JEE Main - 15th April 2018>Q 62

MEDIUM

JEE Main

IMPORTANT

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If $λ \in R$ is such that the sum of the cubes of the roots of the equation $x^{2} + (2 - λ) x + (10 - λ) = 0$ is minimum, then the magnitude of the difference of the roots of this equation is :

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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 - 15th April 2018>Q 63

If

\tan A

and

\tan B

are the roots of the quadratic equation

3 x^{2} - 10 x - 25 = 0

, then the value of

3 \sin^{2} (A + B) - 10 \sin (A + B) \cos (A + B) - 25 \cos^{2} (A + B)

is :

EASY

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 2 - Quadratic Equations>JEE Main - 16th April 2018>Q 64

Let

p, q

and

r

be real numbers

(p \neq q, r \neq 0)

, such that the roots of the equation

\frac{1}{x + p} + \frac{1}{x + q} = \frac{1}{r}

are equal in magnitude but opposite in sign, then the sum of squares of these roots is equal to

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 2 - Quadratic Equations>JEE Main - 8th April 2017>Q 65

Let

p (x)

be a quadratic polynomial such that

p (0) = 1 .

If

p (x)

leaves remainder

4

when divided by

x - 1

and it leaves remainder

6

when divided by

x + 1

then:

MEDIUM

JEE Main

IMPORTANT

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

The sum of all the real values of

x

Satisfying the equation

2^{(x - 1) (x^{2} + 5 x - 50)} = 1

is:

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

) :