Request a call back

# CBSE Class 10 Maths Revision Notes for Quadratic Equations

Does the sound of Class 10 Maths intrigue you? Or, does it scare you away? All of these happen because it's not easy to handle the Board pressure for CBSE Class 10. But, we will surely help you to tackle the syllabus for Class 10 Maths by providing you with the Class 10 Revision NotesClass 10 Textbook SolutionsClass 10 Tests for all of the chapters available in CBSE Class 10 Maths. We know that scoring more marks in CBSE Class 10 Maths has never been this easy before. But, by referring to all of the study materials we provide at TopperLearning, you can easily score more marks in the Class 10 board examination.

The study materials are created by our subject experts that we offer for CBSE Class 10, very well know the syllabus and essential facts of CBSE Class 10. These study materials will help you understand all the CBSE Class 10 Maths concepts as we focus on providing solutions that simplify a subject's complex fundamentals. At TopperLearning, we believe in delivering quality solutions at a low cost, and we strictly follow the latest CBSE Class 10 syllabus. We make sure that these study materials are revised from time to time. Our TopperLearning packages involve all the study resources for CBSE Class 10, such as Solved question papersvideo lessons and revision notes to help you score high marks. We also provide you with the updated NCERT textbook Solutions and RD Sharma textbook solutions, which provide students with step-by-step explanations.

Our study materials have also introduced the Case Study Based Questions for CBSE Class 10 of all the chapters available in Class 10. These questions are designed based on the latest syllabus of CBSE Class 10.

So why wait when you can quickly get the CBSE class 10 plans.

If p(x) is a quadratic polynomial, then p(x) = 0 is called a quadratic equation.

The general or standard form of a quadratic equation, in the variable x, is given by ax2 + bx + c = 0, where a, b, c are real numbers and a ≠ 0.

2. Roots of the quadratic equation
• The value of x that satisfies an equation is called the zeroes or roots of the equation.
• A real number α is said to be a solution/root of the quadratic equation ax2 + bx + c = 0 if aα2 + bα + c = 0.
• A quadratic equation has at most two roots.

3. A quadratic equation can be solved by following algebraic methods:
i. Splitting the middle term (factorization)
ii. Completing squares

4. Splitting the middle term (or factorization) method
• If ax2 + bx + c, a ≠ 0, can be reduced to the product of two linear factors, then the roots of the quadratic equation ax2 + bx + c = 0 can be found by equating each factor to zero.
• Steps involved in solving quadratic equation by splitting the middle term (or factorization) method:

Step 1: Find the product ac.

Step 2: Find the factors of ‘ac’ that add to up to b, using the following criteria:
i. If ac > 0 and b > 0, then both the factors are positive.
ii. If ac > 0 and b < 0, then both the factors are negative.
iii. If ac < 0 and b > 0, then larger factor is positive and smaller factor is negative.
iv. If ac < 0 and b < 0, then larger factor is negative and smaller factor is positive.

Step 3: Split the middle term into two parts using the factors obtained in the above step.

Step 4: Factorize the quadratic equation obtained in the above step by grouping method. Two factors will be obtained.

Step 5: Equate each of the linear factors to zero to get the value of x.

5. Completing the square method

• Any quadratic equation can be converted to the form (x + a)2 – b2 = 0 or (x – a)2 + b2 = 0 by adding and subtracting the constant term. This method of finding the roots of quadratic equation is called the method of completing the square.
• The steps involved in solving a quadratic equation by completing the square, are as follows:

Step 1: Make the coefficient of x2 unity.

Step 2: Express the coefficient of x in the form 2 × x × p.

Step 3: Add and subtract the square of p.

Step 4: Use the square identity (a + b)2 or (a – b)2 to obtain the quadratic equation in the required form (x + a)2 - b2 = 0 or (x – a)2 + b2 = 0.

Step 5: Take the constant term to the other side of the equation.

Step 6: Take the square root on both the sides of the obtained equation to get the roots of the given quadratic equation.

The roots of a quadratic equation ax+ bx + c = 0 (a ≠ 0 )can be calculated by using the quadratic formula:

If b2 – 4ac < 0, then equation does not have real roots.

7. Discriminant of a quadratic equation

For the quadratic equation ax2 + bx + c = 0, a ≠ 0, the expression b2 - 4ac is known as discriminant.

8. Nature of the roots of a quadratic equation:
i. If b2 – 4ac > 0, the quadratic equation has two distinct real roots.
ii. If b2 – 4ac = 0, the quadratic equation has two equal real roots.
iii. If b2 – 4ac < 0, the quadratic equation has no real roots.

9. There are many equations which are not in the quadratic form but can be reduced to the quadratic form by simplifications.

• The applications of quadratic equation can be utilized in solving real life problems.
• Following points can be helpful in solving word problems:
i. Every two digit number ‘xy’ where x is a ten’s place and y is a unit’s place can be expressed as xy=10x+y .

ii. Downstream: It means that the boat is running in the direction of the stream
Upstream: It means that the boat is running in the opposite direction of the stream
Thus, if
Speed of boat in still water is x km/h
And the speed of stream is y km/h
Then the speed of boat downstream will be (x + y) km/h and in upstream it will be (x − y) km/h.

iii. If a person takes x days to finish a work, then his one day's work =

## Why to choose our CBSE Class 10 Maths Study Materials?

• Contain 950+ video lessons, 200+ revision notes, 8500+ questions and 15+ sample papers
• Based on the latest CBSE syllabus
• Free textbook solutions & doubt-solving sessions
• Ideal for quick revision
• Help score more marks in the examination
• Increase paper-solving speed and confidence with weekly tests