1.these are of many types but we are concerned with quadratic and cubic mainly.

2.for :ax^2 +bx+c=0,to solve these questions some points to remember:

a)the given eqn has MAX 2 distinct roots(real or imaginary)depending upon D.

b)find D(discriminant) ie D=b^2-4ac

NOW if D=0 both roots are real and equal

if D>0 both roots are real but distinct

if D<0 then both roots are imaginary(NOTE:Imaginary roots are in conjugate form if if one root is 2+3i,then other must be 2-3i)

NOW if inequation is given in the form of ax^2+bx+c> OR<0 then how can WE SOLVE

soln: 1.Make the sign of "a" POSITIVE in above equation(if already a is positive then it's ok ELSE multiply the above equation by -1 and change the inequality sign as well)

NOTE:in 99 % of inequality questions we can always make the factors of the inequation and put in the form of (x-X)(x-Y)>or<0 AS THE CASE MAY BE.(suppose XNOW draw the number line and mark X and Y on them.In this way the no. line is divided into three parts ie :

(-infinity,X ), (X,Y), (Y,+infinity)

putting the signs alternatively from the right side,starting from POSITIVE..then negative ..then positive.

if (x-X))x-Y)>0 it means our answer lies in POSITIVE sections of the no. line ie

x belongs to(-infinity,X) UNION (Y,infinity)

if (x-X)(x-Y)<0 then answer is x belongs to(X,Y)

NOW we will know about the bature of parabola opening upwards or downwards and find MAX or MIN value thereof.

## Topics
Covered

Equations And Inequations

Nature Of Roots

Graphical Representation

Max And Min Value Of The Equation

In All The IIT And AIEEE 2 To 3 Questions Completed Thoroughly

## Who
should attend

## Pre-requisites

## What
you need to bring

## Key
Takeaways

2.for :ax^2 +bx+c=0,to solve these questions some points to remember:

a)the given eqn has MAX 2 distinct roots(real or imaginary)depending upon D.

b)find D(discriminant) ie D=b^2-4ac

NOW if D=0 both roots are real and equal

if D>0 both roots are real but distinct

if D<0 then both roots are imaginary(NOTE:Imaginary roots are in conjugate form if if one root is 2+3i,then other must be 2-3i)

NOW if inequation is given in the form of ax^2+bx+c> OR<0 then how can WE SOLVE

soln: 1.Make the sign of "a" POSITIVE in above equation(if already a is positive then it's ok ELSE multiply the above equation by -1 and change the inequality sign as well)

NOTE:in 99 % of inequality questions we can always make the factors of the inequation and put in the form of (x-X)(x-Y)>or<0 AS THE CASE MAY BE.(suppose X

(-infinity,X ), (X,Y), (Y,+infinity)

putting the signs alternatively from the right side,starting from POSITIVE..then negative ..then positive.

if (x-X))x-Y)>0 it means our answer lies in POSITIVE sections of the no. line ie

x belongs to(-infinity,X) UNION (Y,infinity)

if (x-X)(x-Y)<0 then answer is x belongs to(X,Y)

NOW we will know about the bature of parabola opening upwards or downwards and find MAX or MIN value thereof.

Nature Of Roots

Graphical Representation

Max And Min Value Of The Equation

In All The IIT And AIEEE 2 To 3 Questions Completed Thoroughly

All Those Students Who Want To Prepare For Engineering Entrances Such As IIT And AIEEE And Others

NOTHING REQUIRED ..

everything is managed in the class.BT the sudent must be attentive during session/

nothing except a pen and notebook.

1.Mathematical Formulation Of Any Equation And In equation

2.Max And Min Value Of Any Function.Etc

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BE FROM DELHI COLLEGE OF ENGINEERING

2 YEAR PLUS EXPERIENCE IN PREPARING STUDENTS FOR IIT JEE AND AIEEE

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