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

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JEE Main

IMPORTANT

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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

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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 - 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

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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

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IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 2 - Quadratic Equations>JEE Main - 28 July 2022 Shift 2>Q 94

Let

S = \{x \in [- 6, 3] - \{- 2, 2\} : \frac{|x + 3| - 1}{|x| - 2} \geq 0\}

and

T = \{x \in Z : x^{2} - 7 |x| + 9 \leq 0\}

. Then the number of elements in

S \cap T

is

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IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 2 - Quadratic Equations>JEE Main - 28 July 2022 Shift 2>Q 95

Let

α, β

be the roots of the equation

x^{2} - \sqrt{2} x + \sqrt{6} = 0

and

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

be the roots of the equation

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

. Then the roots of the equation

x^{2} - (a + b - 2) x + (a + b + 2) = 0

are :

MEDIUM

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IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 2 - Quadratic Equations>JEE Main - 29 July 2022 Shift 2>Q 96

Let

α, β (α > β)

be the roots of the quadratic equation

x^{2} - x - 4 = 0

. If

P_{n} = α^{n} - β^{n}, n \in ℕ

, then

\frac{P_{15} P_{16} - P_{14} P_{16} - P_{15}^{2} + P_{14} P_{15}}{P_{13} P_{14}}

is equal to _____.