Quadratic formula
(For IIT-JEE Preparation)
IITians at your home
ISO 9001:2008 Certified
India's No. 1 Online Academy
Contact: +91-9555288846
Quadratic formula

Consider the quadratic equation ax2 + bx + c = 0 (a ≠ 0). Dividing throughout by a, we get
quadratic formula to find roots of the equation This is the same as
quadratic formula So, the roots of the given equation are the same as those of
quadratic formula to find roots of the equation If quadratic formula , then by taking the square roots in (1), we get
quadratic formula to find roots of the equation Therefore,
quadratic formula So, the roots of ax2 + bx + c = 0 are roots of quadratic equations , if b2 – 4ac ≥ 0. If b2 –4ac < 0, the equation will have no real roots.

Thus, if quadratic formula , then the roots of the quadratic equation ax2 + bx + c = 0 are given by roots of quadratic equations by quadratic formula .

This formula for finding the roots of a quadratic equation is known as the quadratic formula.

Example: Find two consecutive odd positive integers, sum of whose squares is 290.
Solution: Let the smaller of the two consecutive odd positive integers be x. Then, the second integer will be x + 2. According to the question,
roots of equation of quadratic formula which is a quadratic equation in x.
Using the quadratic formula, we get
quadratic formula But x is given to be an odd positive integer. Therefore, x ≠ – 13, x = 11.
Thus, the two consecutive odd integers are 11 and 13.
Check : 112 + 132 = 121 + 169 = 290.

Example: Find the roots of the following quadratic equations, if they exist, using the quadratic formula:
roots of quadratic equation by quadratic formula
quadratic formula Therefore, quadratic formula
So, the roots are 2/3 and 1.
(ii) x2 + 4x + 5 = 0. Here, a = 1, b = 4, c = 5. So, b2 – 4ac = 16 – 20 = – 4 < 0.
Since the square of a real number cannot be negative, therefore quadratic formula will not have any real value.
So, there are no real roots for the given equation.
quadratic formula So,
quadratic formula Therefore,
quadratic formula So, the roots are quadratic formula

Next Topic : Nature of roots
Do you like this Topic?
Share it on

IIT JEE Maths Study Material

Skip Navigation Links.
Collapse MathsMaths
Collapse AlgebraAlgebra
Expand SetsSets
Expand Sequences and seriesSequences and series
Expand Complex NumbersComplex Numbers
Expand Quadratic EquationsQuadratic Equations
Expand Linear inequalitiesLinear inequalities
Expand Permutations and CombinationsPermutations and Combinations
Expand ProbabilityProbability
Expand Binomial theoremBinomial theorem
Expand Matrices and determinantsMatrices and determinants
Collapse TrignometryTrignometry
Collapse CalculusCalculus
Expand Relations and FunctionsRelations and Functions
Expand Limits and DerivativesLimits and Derivatives
Expand Continuity and DifferentiabilityContinuity and Differentiability
Expand Applications of derivativesApplications of derivatives
Expand Integral calculusIntegral calculus
Expand Application of integralsApplication of integrals
Expand Differential equationsDifferential equations
Collapse Coordinate GeometryCoordinate Geometry
Vector and 3D Geometry

Free IIT JEE Study Material

  • Online Classroom Program

    • IITians @ Your Home, Attend Classes directly from Home
    • Two way interaction between Teacher and Students
    • Zero Travel Time or Cost involved, No Hidden Charges
    • Small Batch Sizes, Maximum of 12-15 Students
    • Golden Opportunity to be trained by IITians and NITians
    • All you need is a Computer / Laptop & Internet Connection
    Try Free Demo Class IIT JEE Online Classes
  • 1 on 1 Online Class

    • IITians @ your Home for 1 on 1 Class
    • Two way Communication between Teacher and Student
    • Special Doubt Removal & Problem solving Sessions
    • Customize the Course as per your desire - Duration, Timing, Faculty etc
    • All faculties are IITians and NITians
    • All you need is a Computer / Laptop & Internet Connection
    Try Free Demo Class IIT JEE 1 on 1 Online Classes
  • Correspondence Course Details

    • 600 Hours of Recorded Lectures by IITians and NITians
    • Best Study Material comprising all Concepts and Tricks
    • 10000+ Solved Question Bank + 250 Hours of Video Solutions
    • Complete NCERT solutions + 150 Hours of NCERT Video Solutions
    • Last 30 years JEE chapterwise video solutions
    • 100% Original Material prepared by JEE Experts
    Register for Free Now IIT JEE Correspondence Courses
  • AITS for JEE Main and JEE Advanced

    Register for Free Now JEE Test Series
Welcome to Kshitij Education India

Kshitij Education India as an organisation is immensely grateful to society at large and has made efforts to contribute to the Indian Education system. The free study material section of our website can be deemed as a treasure of resources sufficient for an aspirant to clear JEE Mains. Kshitij provides past year solutions of IIT, AIEEE, JEE Mains and Advanced in its free study material section. Our faculty members put in best efforts to explain each and every question in the best possible manner. Online IIT JEE Free Study Material section also features a collection of over 10,000 pages of study resources covering the entire IIT JEE curriculum. Our discussion forum stimulates a student intellectually with over 5000 threads of IIT discussion topics.

Please enter the Email Id and Contact number of the person to whom you would like to refer www.kshitij-iitjee.com

Welcome to Kshitij Education India
Our Guarantee:
  1. We're so sure you'll have the time of your life with us, we back our courses with a 100% Satisfaction Guarantee.
  2. If for any reason you aren't 100% satisfied with your classes in first 7 days, just let us know and we'll refund your fees. No questions asked.*
  3. And based on your feedback, we will take the necessary steps to ensure we never repeat any mistakes as such.

* It is mandatory to attend first 7 days of live classes and than if you found any valid reason to step back you can request us for refund.

Live Chat