Quadratic Equation -A complete course on Quadratic Equations

Name: Quadratic Equation -A complete course on Quadratic Equations
Rating: 4.5 (14 reviews)

A course on Quadratic Equations that boosts your confidence and inspires you to solve Algebra problems with an ease.

Created bySandeep Kumar Mathur

Last updated 7/2026

English

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What you'll learn

Introduction to Quadratic Equations
Methods of solving Quadratic Equations
Quadratic Formula and Theorem for roots
Nature of Roots
Relation between roots and formation of equation
Word Problems
Condition for common roots and symmetric functions
Solution of questions asked in various competition exams
Quiz and problem sheets for self evaluation

Course content

11 sections • 116 lectures • 10h 9m total length

Introduction6:20
Explore the fundamentals of quadratic equations, including the standard form ax^2+bx+c=0 with a≠0, solving for roots, understanding root nature, graphing, and competition-focused practice.
Example-18:39
Example-1
Example- 27:41
Example-34:07
Example-44:03
Example 56:26
Theorem for number of roots of a Quadratic11:11
This video lecture describes the theorem that a quadratic equation cannot have more than two roots.

Methods of solving Quadratic Equations(Factorisation Method)6:47
This video explains the methods for solving quadratic equations.
Example-11:09
Example-23:21
Example-2
Example 33:57
This lecture shows how to convert a quadratic to standard form, split the middle term, and factor to find the roots x = 5/2 or x = 8/3.
Example-42:55
Factorize the quadratic by splitting the middle term, group to reveal a repeated factor, and find equal roots at x = 3/2.
Example-54:58
Cross-multiply the equation to form a quadratic, simplify to x^2-4x-5=0, factor to (x-5)(x+1), and find x=5 or x=-1.
Method of Completing the Square7:48
Example-14:14
Solving x^2 -10x -2 = 0 by completing the square forms the perfect square (x-5)^2 = 27 and yields the roots 5 ± 3√3.
Example-25:05
Learn to solve 9x^2 - 15x + 6 = 0 by completing the square, dividing by nine to set x^2 coefficient to one, obtaining roots 1 and 2/3.
Example-33:46
Method of Quadratic Formula9:23
Example-13:34
Example-23:29
Example-34:23
Example-45:29
Example-56:41
Clear denominators with the LCM to turn the equation into 2x^2 -15x +25 = 0, then apply the quadratic formula to obtain roots 5 and 5/2, with x ≠ 2,4.
Discriminant2:52
Example - 16:38
Example - 21:49
Example - 2

Nature of Roots10:12
This lecture discusses how can we find out the nature of roots depending upon the value of discriminant.
Example-12:18
Example-23:55
Example-32:27
Example-3
Example-43:53
Example-4
Example 52:39
Example 63:56
Example 76:44
Example 86:15
Example - 93:45
Example-103:48
Example-10
Example-112:55
Example-11
Example-125:15
Example-133:49
Example-144:43
The lecture derives that for the quadratic (1+m^2)x^2 + 2mcx + (c^2 - a^2) = 0, equal roots require the discriminant to be zero, leading to c^2 = a^2(1+m^2).
Example-154:00

Relation between the Roots and coefficients8:32
This lecture explains the relation between the roots and the coefficients .
Example - 12:10
Example 27:08
Example - 32:45
Example - 3
Example - 44:53
Example-57:44
Example-5
Example-62:37
Example-6
Example-77:15
Formation of a quadratic equation7:23
Example-11:42
Example-22:08
Example-33:09
Form the quadratic with complex conjugate roots 3-2i and 3+2i by using their sum 6 and product 13, yielding x^2-6x+13=0.
Example-410:21
Example-54:11
Example-65:10
Demonstrates that the quadratic with roots q/(p - alpha) and q/(p - beta) has sum p and product q, yielding x^2 - p x + q = 0.
Quiz

Example - 15:46
Example - 1
Example-23:47
Example - 2
Example - 34:07
Solve for two consecutive even numbers whose squares sum to 340. Let the numbers be x and x+2; set x^2+(x+2)^2=340 and obtain 12 and 14.
Example 44:47
Example-56:03
Example-5
Example-64:55
Set sister's age as x and girl's as 2x. Four years later the product equals 160, leading to x = 6, so sister is 6 and the girl is 12.
Example-76:11
Example-84:39
Solve the quadratic L^2 - 41L + 400 = 0 to find the rectangular field’s dimensions: length 25 m and breadth 16 m.
Example-95:48
Solve for the usual speed given 3 km in less time when speed is 1 km/h faster; use distance equals speed times time and solve x^2+x-12=0, yielding x=3 km/h.
Example-107:26
Example - 117:21
Example - 11
Example-129:21

Symmetric Expressions of Roots of a Quadratic Equation8:49
Explore symmetric expressions of quadratic roots, swapping alpha and beta leaves expressions unchanged, and learn to express alpha^2+beta^2, alpha^3+beta^3, and related terms using alpha+beta and alpha beta.
Example-13:17
Example-210:09
Derive expressions in terms of a, b, c from a quadratic with roots alpha and beta, using sum and product relations to obtain first expression b/(ac) and second -2/a.
Example-38:49
Example-49:53

Example-17:08
Solve a radical equation reducible to a quadratic by squaring both sides, forming x^2 -6x +5 = 0 to yield x = 5 or 1, with verification.
Example-212:00
Example-35:44
Example-43:45
Example-515:26
Example-64:50
Example-75:27
Derive the equation with roots (alpha-1)/(alpha+1) and (beta-1)/(beta+1) for the given quadratic x^2-2x+3=0 by computing their sum and product, yielding 3x^2-2x+1=0.
Example-83:03
Example-93:04
Determine the minimum value of the quadratic 2x^2 - 3x + 1 for real x by using the discriminant, yielding y = -1/8 as the minimum.

Example-14:15
Example-21:25
Example-32:44
Solve the infinite nested radical by setting x = sqrt(2 + x) and squaring to get x^2 = 2 + x, leading to x = 2 after rejecting minus one.
Example-42:43
Substitute y = x^(1/3) to convert the equation into a quadratic, solve for y, then obtain x = -8 or 1.
Example-53:38
Example-611:08
Use the quadratic formula with a = p - q, b = q - r, c = r - p; roots are (r - p)/(p - q) and 1.
Example-73:52
Example-82:09
Example-97:27
Analyze when a quadratic in x has two rational factors by using the discriminant and a perfect-square form, and find m values of -2 and 6.
Example-103:08
Example-112:04
Factor the quadratic in |x|: |x|^2−3|x|+2=0 into (|x|−2)(|x|−1)=0, giving |x|=2 or |x|=1, hence x=±2 or ±1, four real solutions.
Example-121:19
Example-132:11
Example-141:14

Requirements

Elementary algebra like factorisation,linear equations etc.
A keen interest to learn the topic is needed

Description

Quadratic equations form a cornerstone of algebraic study, frequently appearing in competitive examinations. This comprehensive course caters to learners of all levels, from those encountering the subject for the first time to those seeking advanced understanding.

The curriculum meticulously explores fundamental concepts, beginning with an introduction to quadratic equations and progressing to various solution methods. A thorough examination of the quadratic formula and theorems related to roots is provided, alongside a detailed analysis of the nature of roots. The course further elucidates the relationship between roots and the formation of equations, and tackles word problems that apply these principles.

Advanced topics, including conditions for common roots and symmetric functions, are also covered, culminating in a dedicated "Competition Corner" designed to sharpen problem-solving skills for competitive exams.

This resource is invaluable for students in grades 10 through 12, as well as those preparing for examinations like the IIT JEE and NDA. To enhance comprehension, numerous illustrative examples are incorporated, and the content is presented in a user-friendly, uncluttered format to minimize student stress.

Each section and problem is structured logically and engagingly, fostering a genuine interest in mathematics. Self-evaluation is facilitated through quizzes and problem sheets.

This course aims to cultivate a deeper understanding of quadratic equations and bolster student confidence.

Join now to embark on a rewarding learning journey.

Who this course is for:

Students perusing class 10th,11th and 12th & preparing competitions like IIT JEE,NDA ,MCA entrance etc.

Quadratic Equation -A complete course on Quadratic Equations

What you'll learn

Explore related topics

Course content

Introduction7 lectures • 48min

Solving the Quadratic Equations19 lectures • 1hr 28min

Nature of roots the equations16 lectures • 1hr 11min

Relation between roots and formation of equation15 lectures • 1hr 17min

Word Problems12 lectures • 1hr 10min

Symmetric Expressions of Roots of a Quadratic Equation5 lectures • 41min

Condition for common roots6 lectures • 42min

Miscellaneous Problems9 lectures • 1hr

Objective Questions on Quadratic Equations14 lectures • 49min

Quizes0

Requirements

Description

Who this course is for: