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

HARD

JEE Main

IMPORTANT

Earn 100

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 _____.

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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 - 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-

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 2 - Quadratic Equations>JEE Main - 26 July 2022 Shift 2>Q 90

The minimum value of the sum of the squares of the roots of

x^{2} + (3 - a) x = 2 a - 1

is

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 2 - Quadratic Equations>JEE Main - 27 July 2022 Shift 2>Q 91

If

α, β

are the roots of the equation

x^{2} - (5 + 3^{\sqrt{\log_{3} 5}} - 5^{\sqrt{\log_{5} 3}}) x + 3 (3^{{(\log_{3} 5)}^{\frac{1}{3}}} - 5^{{(\log_{5} 3)}^{\frac{2}{3}}} - 1) = 0

then the equation, whose roots are

α + \frac{1}{β}

and

β + \frac{1}{α}

,

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 2 - Quadratic Equations>JEE Main - 28 July 2022 Shift 1>Q 92

For

p, q \in R

, consider the real valued function

f (x) = {(x - p)}^{2} - q, x \in R

and

q > 0

. Let

a_{1}, a_{2}, a_{3}

and

a_{4}

be in an arithmetic progression with mean

p

and positive common difference. If

|f (a_{i})| = 500

for all

i = 1, 2, 3, 4

, then the absolute difference between the roots of

f (x) = 0

is

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 2 - Quadratic Equations>JEE Main - 28 July 2022 Shift 1>Q 93

The sum of all real values of

x

for which

\frac{3 x^{2} - 9 x + 17}{x^{2} + 3 x + 10} = \frac{5 x^{2} - 7 x + 19}{3 x^{2} + 5 x + 12}

is equal to