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Quadratic Formula

Quadratic Equations II - Concepts

Quadratic Formula

Nature of Roots of Quadratic Polynomial

Problems Involving Ratio Of Speed

Problems Involving Average Speed

Problems Based on Speed

Problems Involving Speed of Boat In Still Water

Problems Involving Boat Moving Upstream

Problems Involving Boat Moving Downstream

Solving Statement For Upstream And Downstream

Single Pipe Filling The Tank

Single Pipe Emptying The Tank

Multiple Pipes Filling The Tank

Pipes Emptying and Filling The Tank

Solving Statements Involving Pipes

Problems Involving Moving Train And Stationary Person

Problems Involving Train Crossing Bridge or Platform

Problems Involving Crossing Of Trains Moving In Same Direction

Problems Involving Crossing Of Trains Moving In Opposite Direction

Problems Involving Moving Train And Moving Person

Problems Involving Relative Speed

Class - 10th IMO Subjects

Concept Explanation

Quadratic Formula

The Quadratic Formula: For a quadratic equation

$large ax^2+bx+c = 0, ;where; aneq 0$

Using Completing the square method we can find the roots

$large ax^2+bx=-c$

$large x^2+frac{b}{a}x=-frac{c}{a}$

$large x^2+2left ( frac{b}{2a} right )x + left (frac{b}{2a} right )^2=-frac{c}{a}+ left (frac{b}{2a} right )^2$

$large left (x+ frac{b}{2a} right )^2=-frac{c}{a}+ left (frac{b^2}{4a^2} right )$

$large left (x+ frac{b}{2a} right )^2=left(frac{b^2-4ac}{4a^2} right )$

$large left (x+ frac{b}{2a} right )=pm left (frac{sqrt{b^2-4ac}}{2a} right )$

$large x=- frac{b}{2a} pm left (frac{sqrt{b^2-4ac}}{2a} right )$

$large x=frac{-bpm sqrt{b^2-4ac}}{2a}$

$large x=frac{-bpm sqrt{D}}{2a}, ;where; D=b^2-4ac$

Example: Find the solution of quadratic equation:

$large -3x^2+5x-2=0$

Solution: Comparing with standard form we get

a= -3, b= 5 and c= -2

$large D= b^2-4ac= (5)^2-4 X (-3) X (-2)= 25-24=1$

So the solutions are

$large x=frac{-(5)pm sqrt{1}}{2(-3)}$

$large x=frac{-5pm 1}{-6}$

$large Either;x=frac{-5-1}{-6}; or; x=frac{-5+1}{-6}$

$large Either;x= 1; or; x=frac{2}{3}$

Sample Questions

(More Questions for each concept available in Login)

Question : 1

Solve the quadratic equation? $x^2-9x+18=0$
A. 3 0r 9	B. 6 or 3	C. 10 0r 3	D. 1 or 5
Right Option : B
View Explanation

Question : 2

Find the value of discriminant for the equation $2x^2+5x+6=0$
A. -22	B. 23	C. -23	D. None of these
Right Option : C
View Explanation

Question : 3

Find the value of the discriminant for the quadratic equation $frac{2}{7}x^2+5x+42=0$
A. -22		B. -23
C. -28		D. None of these
Right Option : B
View Explanation

Video Link - Have a look !!!

Language - English

Chapters

Real Numbers I

Real Numbers II

Pair of Linear Equations I

Pair of Linear Equations II

Polynomial I

Polynomials II

Quadratic Equations I

Quadratic Equations II

Introduction to Trigonometry I

Introduction to Trigonometry II

Arithmetic Progression I

Arithmetic Progression II

Triangles I

Triangles II

Some Applications of Trigonometry

Coordinate Geometry I

Coordinate Geometry II

Introduction to Trigonometry

Direct and Inverse Variation

Surface Area and Volume I

Surface Area and Volume II

Areas Related to Circles

Content / Category

IMO-Mathematics Olympiad

Central Government Service

ISO - Science Olympiads

State Government Services

Banking And Insurance

Railways & Metro Services

MBA Entrance

Law Entrance

English Proficiency

Reasoning Proficiency

Computer Proficiency

Navodaya Entrance 6th & 9th

Sainik School Entrance

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Quadratic Formula

Quadratic Formula

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Prisha Gupta

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