EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 2 - Quadratic Equations>JEE Main - 25 June 2022 Shift 1>Q 81

HARD

JEE Main

IMPORTANT

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For a natural number $n$ , let $α_{n} = 19^{n} - 12^{n}$ . Then, the value of $\frac{31 α_{9} - α_{10}}{57 α_{8}}$ 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 - 25 June 2022 Shift 2>Q 82

Let

a, b \in R

be such that the equation

a x^{2} - 2 b x + 15 = 0

has repeated root

α

and if

α

and

β

are the roots of the equation

x^{2} - 2 b x + 21 = 0

, then

α^{2} + β^{2}

is equal to:

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 2 - Quadratic Equations>JEE Main - 26 June 2022 Shift 2>Q 83

If

p

and

q

are real number such that

p + q = 3, p^{4} + q^{4} = 369

, then the value of

{(\frac{1}{p} + \frac{1}{q})}^{- 2}

is equal to

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 2 - Quadratic Equations>JEE Main - 26 June 2022 Shift 1>Q 84

The sum of the cubes of all the roots of the equation

x^{4} - 3 x^{3} - 2 x^{2} + 3 x + 1 = 10

is _____.

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 2 - Quadratic Equations>JEE Main - 27 June 2022 Shift 1>Q 85

If the sum of all the roots of the equation

e^{2 x} - 11 e^{x} - 45 e^{- x} + \frac{81}{2} = 0

is

\log_{e} P

, then

P

is equal to _____.

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 2 - Quadratic Equations>JEE Main - 27 June 2022 Shift 2>Q 86

Let

α, β

be the roots of the equation

x^{2} - 4 λ x + 5 = 0

and

α, γ

be the roots of the equation

x^{2} - (3 \sqrt{2} + 2 \sqrt{3}) x + 7 + 3 λ \sqrt{3} = 0

. If

β + γ = 3 \sqrt{2}

, then

{(α + 2 β + γ)}^{2}

is equal to

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 2 - Quadratic Equations>JEE Main - 28 June 2022 Shift 1>Q 87

The number of real solutions of the equation

e^{4 x} + 4 e^{3 x} - 58 e^{2 x} + 4 e^{x} + 1 = 0

is _____.

EASY

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 2 - Quadratic Equations>JEE Main - 28 June 2022 Shift 2>Q 88

Let

f (x)

be a quadratic polynomial such that

f (- 2)

+ f (3) = 0

. If one of the roots of

f (x) = 0

is

- 1

, then the sum of the roots of

f (x) = 0

is equal to

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 2 - Quadratic Equations>JEE Main - 26 July 2022 Shift 1>Q 89

If for some

p, q, r \in R

, not all have same sign, one of the roots of the equation

(p^{2} + q^{2}) x^{2} - 2 q (p + r) x + q^{2} + r^{2} = 0

is also a root of the equation

x^{2} + 2 x - 8 = 0

, then

\frac{q^{2} + r^{2}}{p^{2}}

is equal to-