EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 2 - Quadratic Equations>JEE Advanced Paper 1 - 2020>Q 5

HARD

JEE Advanced

IMPORTANT

Earn 100

Suppose $a, b$ denote the distinct real roots of the quadratic polynomial $x^{2} + 20 x - 2020$ and suppose $c, d$ denote the distinct complex roots of the quadratic polynomial $x^{2} - 20 x + 2020$ . Then the value of $a c (a - c) + a d (a - d) + b c (b - c) + b d (b - d)$ is equal to

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Important Questions on Quadratic Equations

HARD

JEE Advanced

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 2 - Quadratic Equations>JEE Advanced Paper 1 - 2019>Q 6

Let

α

and

β

be the roots of

x^{2} - x - 1 = 0,

with

α > β .

For all positive integers

n,

define

a_{n} = \frac{α^{n} - β^{n}}{α - β}, n \geq 1

b_{1} = 1

and

b_{n} = a_{n - 1} + a_{n + 1}, n \geq 2 .

Then which of the following options is/are correct?

HARD

JEE Advanced

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 2 - Quadratic Equations>JEE Advanced Paper 1 - 2016>Q 7

Let

- \frac{π}{6} < θ < - \frac{π}{12}

. Suppose

α_{1}

and

β_{1}

are the roots of the equation

x^{2} - 2 x \sec θ + 1 = 0

and

α_{2}

and

β_{2}

are the roots of the equation

x^{2} + 2 x \tan θ - 1 = 0 .

If

α_{1} > β_{1}

and

α_{2} > β_{2}

, then

α_{1} + β_{2}

equals

HARD

JEE Advanced

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 2 - Quadratic Equations>JEE Advanced Paper 1 - 2014>Q 8

Let

a \in R

and let

f : R \to R

be given by

f (x) = x^{5} - 5 x + a,

then