# Quadratic Equations class 10 Notes Mathematics

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## CBSE Guide Quadratic Equations class 10 Notes

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## 10 Mathematics notes Chapter 4 Quadratic Equations

CBSE Class–10 Mathematics
Revision Notes
CHAPTER 04

2. Solution by Factorisation

3. Solution by Completing the Square

4. Nature of Roots

1. The equation $a{x^2} + bx + c$ , $a \ne 0$  is the standard form of a quadratic equation, where a, b and c are real numbers.

$a{x^2} + bx + c = 0,a \ne 0$ is known as Standard form or General form of a quadratic equation.

In other words, we can say that an equation of order (degree) 2 is called a quadratic equation.

2. A real number $\alpha$  is said to be a root of the quadratic equation $a{x^2} + bx + c = 0,a \ne 0$ , ${ a } \ne 0$. If $a{\alpha ^2} + b\alpha + c = 0,$ the zeroes of quadratic polynomial ${\text{a}}{{\text{x}}^2}{\text{ }} + {\text{ bx }} + {\text{ c }}$ and the roots of the the quadratic equation ${\text{a}}{{\text{x}}^2}{\text{ }} + {\text{ bx }} + {\text{ c }} = {\text{ }}0$ are the same.

3. If we can factorise ${\text{a}}{{\text{x}}^2}{\text{ }} + {\text{ bx }} + {\text{ c }} = {\text{ }}0,{\text{ a }} \ne {\text{ }}0$ into product of two linear factors,then the roots of the quadratic equation can be found by equating each factors to zero.

4. The roots of a quadratic equation ${\text{a}}{{\text{x}}^2}{\text{ }} + {\text{ bx }} + {\text{ c }} = {\text{ }}0$, ${ a } \ne 0$ are given by $\frac{{ - b \pm \sqrt {{b^2} - 4ac} }}{{2a}},$provided that ${{\text{b}}^2}-{\text{ 4ac}} \geqslant {\text{ }}0$. It is called Quadratic formula.

5. A quadratic equation ${\text{a}}{{\text{x}}^2}{\text{ }} + {\text{ bx }} + {\text{ c }} = {\text{ }}0$, ${ a } \ne 0$ has :

(a) Two distinct and real roots, if ${b^2} - 4ac\; > \;0.$

(b) Two equal and real roots, if ${b^2} - 4ac\; = \;0.$

(c) Two roots are not real, if ${b^2} - 4ac\; < \;0.$

6. A quadratic equation can also be solved by the method of completing the square.

(i) ${{\text{a}}^2}{\text{ }} + {\text{ 2ab}} + {\text{ }}{{\text{b}}^2}{\text{ }} = {\text{ }}{\left( {{\text{a }} + {\text{b}}} \right)^2}$

(ii) ${{\text{a}}^2}{\text{ - 2ab}} + {\text{ }}{{\text{b}}^2}{\text{ }} = {\text{ }}{\left( {{\text{a - b}}} \right)^2}$

7. Discriminant of the quadratic equation ${\text{a}}{{\text{x}}^2}{\text{ }} + {\text{ bx }} + {\text{ c }} = {\text{ }}0$, ${ a } \ne 0$ is given by $D = {b^2} - 4ac$.

## Quadratic Equations class 10 Notes

• CBSE Revision notes for Class 10 Mathematics PDF
• CBSE Revision notes Class 10 Mathematics – CBSE
• CBSE Revisions notes and Key Points Class 10 Mathematics
• Summary of the NCERT books all chapters in Mathematics class 10
• Short notes for CBSE class 10th Mathematics
• Key notes and chapter summary of Mathematics class 10
• Quick revision notes for CBSE board exams

## CBSE Class-10 Revision Notes and Key Points

Quadratic Equations class 10 Notes. CBSE quick revision note for Class-10 Mathematics, Chemistry, Maths, Biology and other subject are very helpful to revise the whole syllabus during exam days. The revision notes covers all important formulas and concepts given in the chapter. Even if you wish to have an overview of a chapter, quick revision notes are here to do if for you. These notes will certainly save your time during stressful exam days.

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