EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 2 - Quadratic Equations>JEE Main - 9th January 2020 Shift 2>Q 45

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IMPORTANT

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Let $a, b \in R, a \neq 0$ be such that the equation, $a x^{2} - 2 b x + 5 = 0$ has a repeated root $α,$ which is also a root of the equation, $x^{2} - 2 b x - 10 = 0 .$ If $β$ is the other root of this equation, then $α^{2} + β^{2}$ is equal to:

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Important Questions on Quadratic Equations

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JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 2 - Quadratic Equations>JEE Main - 9th April 2019 Shift 1>Q 46

Let

p, q \in Q .

If

2 - \sqrt{3}

is a root of the quadratic equation

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

then

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IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 2 - Quadratic Equations>JEE Main - 9th April 2019 Shift 2>Q 47

If

m

is chosen in the quadratic equation

(m^{2} + 1) x^{2} - 3 x + {(m^{2} + 1)}^{2} = 0

such that the sum of its roots is greatest, then the absolute difference of the cubes of its roots is:

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IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 2 - Quadratic Equations>JEE Main - 9th January 2019 Shift 2>Q 48

The number of all possible positive integral value of

α

for which the roots of the quadratic equation

6 x^{2} - 11 x + α = 0

are rational numbers is:

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 2 - Quadratic Equations>JEE Main - 9th January 2019 Shift 2>Q 49

If both the roots of the quadratic equation

x^{2} - m x + 4 = 0

are real and distinct and they lie in the interval

(1, 5),

then

m

lies in the interval:

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IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 2 - Quadratic Equations>JEE Main - 8th April 2019 Shift 1>Q 50

The sum of the solutions of the equation

|\sqrt{x} - 2| + \sqrt{x} (\sqrt{x} - 4) + 2 = 0, (x > 0)

is equal to

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IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 2 - Quadratic Equations>JEE Main - 8th April 2019 Shift 1>Q 51

If

α

and

β

be the roots of the equation

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

then the least value of

n

for which

{(\frac{α}{β})}^{n} = 1

is

EASY

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IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 2 - Quadratic Equations>JEE Main - 8th April 2019 Shift 2>Q 52

The number of integral values of

m

for which the equation,

(1 + m^{2}) x^{2} - 2 (1 + 3 m) x + (1 + 8 m) = 0

has no real root, is

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IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 2 - Quadratic Equations>JEE Main - 10th April 2019 Shift 1>Q 53

If

α

and

β

are the roots of the quadratic equation

x^{2} + x s i n θ - 2 s i n θ = 0, θ \in (0, \frac{π}{2})

, then

\frac{α^{12} + β^{12}}{(α^{- 12} + β^{- 12}) {. (α - β)}^{24}}

is equal to :