EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 2 - Quadratic Equations>JEE Main - 3 September 2020 Shift 2>Q 31

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IMPORTANT

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The set of all real values of $λ$ for which the quadratic equation $(λ^{2} + 1) x^{2} - 4 λ x + 2 = 0$ always have exactly one root in the interval $(0, 1)$ 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 - 4 September 2020 Shift 2>Q 32

Let

λ \neq 0

be in

R

. If

α

and

β

are the roots of the equation,

x^{2} - x + 2 λ = 0

and

α

and

γ

are the roots of the equation,

3 x^{2} - 10 x + 27 λ = 0,

then

\frac{β γ}{λ}

is equal to:

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JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 2 - Quadratic Equations>JEE Main - 5 September 2020 Shift 1>Q 33

The product of the roots of the equation

9 x^{2} - 18 | x | + 5 = 0

is :

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JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 2 - Quadratic Equations>JEE Main - 5 September 2020 Shift 2>Q 34

If

α

and

β

are the roots of the equation,

7 x^{2} - 3 x - 2 = 0,

then the value of

\frac{α}{1 - α^{2}} + \frac{β}{1 - β^{2}}

is equal to:

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JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 2 - Quadratic Equations>JEE Main - 6 September 2020 Shift 1>Q 35

If

α

and

β

be two roots of the equation

x^{2} - 64 x + 256 = 0 .

Then the value of

{(\frac{α^{3}}{β^{5}})}^{\frac{1}{8}} + {(\frac{β^{3}}{α^{5}})}^{\frac{1}{8}}

is :

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JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 2 - Quadratic Equations>JEE Main - 6 September 2020 Shift 2>Q 36

If

α

and

β

are the roots of the equation

2 x (2 x + 1) = 1

, then

β

is equal to :

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 2 - Quadratic Equations>JEE Main - 7th January 2020 Shift 1>Q 37

Let

α

and

β

be two real roots of the equation

(k + 1) {t a n}^{2} x - \sqrt{2} \cdot λ \tan x = (1 - k),

where

k (\neq - 1)

and

λ

are real numbers. If

{t a n}^{2} (α + β) = 50,

then a value of

λ

is

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 2 - Quadratic Equations>JEE Main - 7th January 2020 Shift 1>Q 38

If the sum of the coefficients of all even powers of

x

in the product

(1 + x + x^{2} + \dots + x^{2 n}) (1 - x + x^{2} - x^{3} + \dots + x^{2 n})

is

61,

then

n

is equal to

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 2 - Quadratic Equations>JEE Main - 7th January 2020 Shift 2>Q 39

Let

α

and

β

be the roots of the equation

x^{2} - x - 1 = 0

. If

P_{k} = {(α)}^{k} + {(β)}^{k}, k \geq 1,

then which one of the following statements is not true?