EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 2 - Quadratic Equations>JEE Main - 27 August 2021 Shift 1>Q 4

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IMPORTANT

Earn 100

The number of distinct real roots of the equation $3 x^{4} + 4 x^{3} - 12 x^{2} + 4 = 0$ 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 - 27 August 2021 Shift 2>Q 5

The set of all values of

k > - 1

, for which the equation

{(3 x^{2} + 4 x + 3)}^{2} - (k + 1) (3 x^{2} + 4 x + 3) (3 x^{2} + 4 x + 2) +

k {(3 x^{2} + 4 x + 2)}^{2} = 0

has real roots, is:

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JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 2 - Quadratic Equations>JEE Main - 31 August 2021 Shift 2>Q 6

The sum of the roots of the equation, $x + 1 - 2 \log_{2} (3 + 2^{x}) + 2 \log_{4} (10 - 2^{- x}) = 0,$ is :

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JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 2 - Quadratic Equations>JEE Main - 1 September 2021 Shift 2>Q 7

The number of pairs

(a, b)

of real numbers, such that whenever

α

is a root of the equation

x^{2} + a x + b = 0, α^{2} - 2

is also a root of this equation, is :

EASY

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 2 - Quadratic Equations>JEE Main - 1 September 2021 Shift 2>Q 8

Let

f (x)

be a polynomial of degree

3

such that

f (k) = - \frac{2}{k}

for

k = 2, 3, 4, 5 .

Then the value of

52 - 10 f (10)

is equal to _____ .

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JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 2 - Quadratic Equations>JEE Main - 20 July 2021 Shift 1>Q 9

If

α

and

β

are the distinct roots of the equation

x^{2} + {(3)}^{\frac{1}{4}} x + 3^{\frac{1}{2}} = 0

, then the value of

α^{96} (α^{12} - 1) + β^{96} (β^{12} - 1)

is equal to:

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 2 - Quadratic Equations>JEE Main - 20 July 2021 Shift 2>Q 10

The number of solutions of the equation

\log_{(x + 1)} (2 x^{2} + 7 x + 5) + \log_{(2 x + 5)} (x + 1)^{2} - 4 = 0, x > 0,

is

EASY

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 2 - Quadratic Equations>JEE Main - 25 July 2021 Shift 1>Q 11

If

α, β

are roots of the equation

x^{2} + 5 (\sqrt{2}) x + 10 = 0, α > β

and

P_{n} = α^{n} - β^{n}

for each positive integer

n,

then the value of

(\frac{P_{17} P_{20} + 5 \sqrt{2} P_{17} P_{19}}{P_{18} P_{19} + 5 \sqrt{2} P_{18}^{2}})

is equal to

EASY

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 2 - Quadratic Equations>JEE Main - 25 July 2021 Shift 2>Q 12

The number of real solutions of the equation,

x^{2} - |x| - 12 = 0

is: