CBSE Class 10 Quadratic Equations Important Formulas and concepts for exams

Read and download the CBSE Class 10 Quadratic Equations Important Formulas and concepts for exams. Designed for 2026-27, this advanced study material provides Class 10 Mathematics students with detailed revision notes, sure-shot questions, and detailed answers. Prepared by expert teachers and they follow the latest CBSE, NCERT, and KVS guidelines to ensure you get best scores.

Chapter 4 Quadratic Equations Study Guide for Class 10 Mathematics

Try using this Class 10 Chapter 4 Quadratic Equations study material to boost your Mathematics knowledge beyond standard classroom textbooks. It offers structured summaries and answered questions to ensure Class 10 students master every core idea.

Chapter 4 Quadratic Equations Summary & Questions for Class 10 Mathematics

CBSE Class 10 Quadratic Equations Important Formulas and concepts for exams. There are many more useful educational material which the students can download in pdf format and use them for studies. Study material like concept maps, important and sure shot question banks, quick to learn flash cards, flow charts, mind maps, teacher notes, important formulas, past examinations question bank, important concepts taught by teachers. Students can download these useful educational material free and use them to get better marks in examinations.  Also refer to other worksheets for the same chapter and other subjects too. Use them for better understanding of the subjects.

POLYNOMIALS

An algebraic expression of the form p(x) = a0 + a1x + a2x2 + a3x3+ …………….anxn, where a ≠  0, is called a polynomial in variable x of degree n.

Here, a0, a1, a2, a3, ………,an are real numbers and each power of x is a non-negative integer. e.g. 3x2  – 5x + 2 is a polynomial of degree 2.

3√ 2 x + is not a polynomial.

• If p(x) is a polynomial in x, the highest power of x in p(x) is called the degree of the polynomial p(x). For example, 4x + 2 is a polynomial in the variable x of degree 1, 2y2– 3y + 4 is a polynomial in the variable y of degree 2,

 • A polynomial of degree 0 is called a constant polynomial.

  • A polynomial p(x) = ax + b of degree 1 is called a linear polynomial.

  • A polynomial p(x) = ax2 + bx + c of degree 2 is called a quadratic polynomial.

  • A polynomial p(x) = ax3 + bx2 + cx + d of degree 3 is called a cubic polynomial.

  • A polynomial p(x) = ax4+ bx3 + cx2 + dx + e of degree 4 is called a bi-quadratic polynomial.

QUADRATIC EQUATION

A polynomial p(x) = ax2 + bx + c of degree 2 is called a quadratic polynomial, then p(x) = 0 is known as quadratic equation.

e.g. 2x2 – 3x + 2 = 0, x2 + 5x + 6 = 0 are quadratic equations.

METHODS TO FIND THE SOLUTION OF QUADRATIC EQUATIONS

Three methods to find the solution of quadratic equation:

1. Factorisation method

2. Method of completing the square

3. Quadratic formula method

FACTORISATION METHOD

Steps to find the solution of given quadratic equation by factorisation

  • Firstly, write the given quadratic equation in standard form ax2 + bx + c = 0.

  • Find two numbers a and b such that sum of a and b is equal to b and product of a and b is equal to ac.

  • Write the middle term bx as αx+βx and factorise it by splitting the middle term and let factors are (x + p) and (x + q) i.e. ax2+ bx + c = 0=›(x + p)(x + q) = 0

 • Now equate reach factor to zero and find the values of x.

 • These values of x are the required roots/solutions of the given quadratic equation.

METHOD OF COMPLETING THE SQUARE

Steps to find the solution of given quadratic equation by Method of completing the square:

  • Firstly, write the given quadratic equation in standard form ax2 + bx + c = 0.

  • Make coefficient of x2 unity by dividing all by a then we get x2+b/ax+c/a=0

  • Shift the constant on RHS and add square of half of the coefficient of x i.e. (b/2a)2 on both sides.

   x2 + b/ax = - c/a x2 +2(b/2a)x + (b/2a)2 = - c/a + (b/2a)2
 
• Write LHS as the perfect square of a binomial expression and simplify RHS.
 
   (x + b/2a)2 = b2-4ac /4a2
 
• Take square root on both sides
 
x + b/2a = ±√b2 -4ac/4a2
 
• Find the value of x by shifting the constant term on RHS i.e.
x = ±√b2-4ac/4a2 -b/2a
 
QUADRATIC FORMULA METHOD
 
Steps to find the solution of given quadratic equation by quadratic formula method:
• Firstly, write the given quadratic equation in standard form ax2 + bx + c = 0.
 
• Write the values of a, b and c by comparing the given equation with standard form.
 
• Find discriminant D = b2 – 4ac. If value of D is negative, then is no real solution i.e. solution does not exist. If value of D≥ 0, then solution exists follow the next step.
 
• Put the value of a, b and D in quadratic formula x = -b ± D /2a and get the required roots/solutions.
 
NATURE OF ROOTS
The roots of the quadratic equation ax2 + bx + c = 0 by quadratic formula are given by x -b= ± √b2-4ac/4a =  -b ±√D /2a
 
where D = b2 - 4ac is called discriminant. The nature of roots depends upon the value of
discriminant D. There are three cases –
Case – I
When D > 0 i.e. b2 - 4ac > 0, then the quadratic equation has two distinct roots. i.e.  -b + √D /2a and  -b -√D /2a
 
Case – II
When D = 0, then the quadratic equation has two equal real roots.
i.e. x = -b /2a  and  -b /2a 
 
Case – III
When D < 0 then there is no real roots exist.

Please click the link below to download CBSE Class 10 Quadratic Equations Important Formulas and concepts for exams.

Free study material for Mathematics

Useful Resources & Notes for Class 10 Mathematics Chapter 4 Quadratic Equations

Core Study Kit: Class 10 Mathematics Chapter 4 Quadratic Equations

Gather all necessary academic resources for Chapter 4 Quadratic Equations on this dedicated page. Formulated in direct alignment with the active 2026 standards for Class 10 Mathematics, the pack offers thorough notes, handy Mind Maps, and exam-focused Sure Shot Questions for CBSE exams. Instructors advise leveraging these assets daily to optimize study speed.

Understanding Marking Schemes with Solved Examples

Our teachers have used the latest official NCERT book for Class 10 Mathematics to prepare these study material. We have included previous year examination questions and also step-by-step solutions to help you understand the marking scheme too. After reading the above chapter notes and solved questions also solve the practice problems and then compare your work with our NCERT solutions for Class 10 Mathematics.

Maximizing Accuracy with Online Assessment Tools

Maximize your grade potential in Class 10 by utilizing Mathematics Sample Papers in tandem with our structured notes. Daily execution of online MCQ Tests for Chapter 4 Quadratic Equations refines precision and pacing. All content across our portal is free and regularly optimized to help Class 10 scholars tackle school assessments with absolute confidence.

FAQs

What is included in the advanced study material for Class 10 Mathematics Chapter 4 Quadratic Equations?

Our advanced study package for Chapter 4 Quadratic Equations includes detailed concepts, diagrams, Mind Maps, and explanation of complex topics to ensure Class 10 students learn as per syllabus for 2026 exams.

How do Mind Maps for Mathematics Chapter 4 Quadratic Equations help in revision?

The Mind Maps provided for Chapter 4 Quadratic Equations act as visual anchors which will help faster recall during high-pressure exams.

Are these Mathematics resources suitable for both classroom teaching and self-study?

Yes, teachers use our Class 10 Mathematics resources for lesson planning as they are in simple language and have lot of solved examples.

Is this advanced study material for Chapter 4 Quadratic Equations free to download in PDF?

Yes, You can download the complete, mobile-friendly PDF of the Mathematics Chapter 4 Quadratic Equations advanced resources for free.

Does this material cover rationalized content for the 2026-27 CBSE session?

Yes, our subject matter experts have updated the Chapter 4 Quadratic Equations material to align with the rationalized NCERT textbooks and have removed deleted topics and added new competency-based questions.