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

EASY

JEE Main

IMPORTANT

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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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Important Questions on Quadratic Equations

MEDIUM

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:

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 2 - Quadratic Equations>JEE Main - 25 July 2021 Shift 2>Q 13

If

a + b + c = 1, a b + b c + c a = 2

and

a b c = 3,

then the value of

a^{4} + b^{4} + c^{4}

is equal to:

EASY

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 2 - Quadratic Equations>JEE Main - 27 July 2021 Shift 1>Q 14

Let

α, β

be two roots of the equation

x^{2} + {(20)}^{1 / 4} x + {(5)}^{1 / 2} = 0

. Then

α^{8} + β^{8}

is equal to

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 2 - Quadratic Equations>JEE Main - 27 July 2021 Shift 2>Q 15

The number of real roots of the equation

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

is equal to

EASY

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 2 - Quadratic Equations>JEE Main 16 March 2021 Shift 1>Q 16

The number of elements in the set

\{x \in R : (| x | - 3) |x + 4| = 6\}

is equal to