EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 2 - Quadratic Equations>JEE Main - 24 Feb 2021 Shift 1>Q 22

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IMPORTANT

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Let $p$ and $q$ be two positive numbers such that $p + q = 2$ and $p^{4} + q^{4} = 272$ . Then $p$ and $q$ are roots of the equation:

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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 - 24 Feb 2021 Shift 2>Q 23

The number of the real roots of the equation

{(x + 1)}^{2} + | x - 5 | = \frac{27}{4}

is ________.

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 2 - Quadratic Equations>JEE Main - 25 Feb 2021 Shift 1>Q 24

The integer

k,

for which the inequality

x^{2} - 2 (3 k - 1) x + 8 k^{2} - 7 > 0

is valid for every

x

in

R

is:

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 2 - Quadratic Equations>JEE Main - 25 Feb 2021 Shift 2>Q 25

Let

α

and

β

be the roots of

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

. If

a_{n} = α^{n} - β^{n}

for

n ⩾ 1

, then the value of

\frac{a_{10} - 2 a_{8}}{3 a_{9}}

is:

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 2 - Quadratic Equations>JEE Main - 26 Feb 2021 Shift 2>Q 26

If the arithmetic mean and the geometric mean of the

p^{th}

and

q^{th}

terms of the sequence

- 16, 8, - 4, 2, \dots

satisfy the equation

4 x^{2} - 9 x + 5 = 0

, then

p + q

is equal to _______.

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 2 - Quadratic Equations>JEE Main - 26 Feb 2021 Shift 2>Q 27

Let

α

and

β

be two real numbers such that

α + β = 1

and

α β = - 1

. Let

p_{n} = {(α)}^{n} + {(β)}^{n}

,

p_{n - 1} = 11

and

p_{n + 1} = 29

for some integer

n ⩾ 1

. Then, the value of

p_{n}^{2}

is______.

EASY

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 2 - Quadratic Equations>JEE Main - 2 September 2020 Shift 1>Q 28

Let

α

and

β

be the roots of the equation,

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

. If

S_{n} = α^{n} + β^{n}, n = 1, 2, 3, . . . .,

then

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 2 - Quadratic Equations>JEE Main - 2 September 2020 Shift 2>Q 29

Let

f (x)

be a quadratic polynomial such that

f (- 1) + f (2) = 0

. If one of the roots of

f (x) = 0

is

3

, then its other root lies in

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 2 - Quadratic Equations>JEE Main - 3 September 2020 Shift 1>Q 30

If

α

and

β

are the roots of the equation

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

and

\frac{1}{α}

and

\frac{1}{β}

are the roots of the equation

2 x^{2} + 2 q x + 1 = 0,

then

(α - \frac{1}{α}) (β - \frac{1}{β}) (α + \frac{1}{β}) (β + \frac{1}{α})

is equal to :