Скачать или смотреть Quadratic Equations- Introduction || ICSE Class 10 Maths

"Quadratic Equations" is an engrossing chapter for both ICSE and CBSE Boards.A quadratic equation is an equation in one variable degree 2 equation.The general form of a quadratic equation is ax²+bx+c = 0 , where x represents an unknown, and a, b, and c represent known numbers, where a ≠ 0. If a = 0, then the equation is linear, not quadratic, as there is no term like x². The numbers a, b, and c are the COEFFICIENTS of the equation and may be distinguished by calling them, respectively, the quadratic coefficient, the linear coefficient and the constant or free term.
The values of x that satisfy the equation are called SOLUTIONS of the equation, and ROOTS or ZEROS of the EXPRESSION on its left-hand side. A quadratic equation has at most two solutions. If there is no REAL solution, there are two complex solutions. If there is only one solution, one says that it is a double roots. A quadratic equation always has two roots, if complex roots are included and a double root is counted for two. A quadratic equation can be factorized into an equivalent equation
Because the quadratic equation involves only one unknown, it is called "UNIVARIATE". The quadratic equation contains only POWERS of x that are non-negative integers, and therefore it is a POLYNOMIAL EQUATION. In particular, it is a SECOND-DEGREE polynomial equation, since the greatest power is two.
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Dear Students.....
In this video, I have discussed on the following topics:

-What is a quadratic equations
-What is the general form of a quadratic equation
-What is the standard form of a quadratic equation
-What are the topics we have to read in quadratic equation
-What are the methods to solve a quadratic equation
-What is a quadratic equation formula to find the value of the variable
-What do you mean by discriminant
-What is the formula to find a discriminant
-Nature of roots and,
-How can decide whether the equation is a quadratic equation or not
Quadratic Equations

Class - 10
Maths
ICSE / CBSE
Chapter Name - Quadratic Equations
Topic - Introduction to Quadratic Equations

Terms used in the video :
-quadratic equation
-general form
-standard form
-nature of the roots

Quadratic Equations :
In algebra, a quadratic equation is any equation that can be rearranged in standard form as ax^{2}+bx+c=0 where x represents an unknown, and a, b, and c represent known numbers, where a ≠ 0. If a = 0, then the equation is linear, not quadratic, as there is no ax^2 term. 
Examples :
6x² + 11x - 35 = 0.

2x² - 4x - 2 = 0.

-4x² - 7x +12 = 0.

20x² -15x - 10 = 0.

x² -x - 3 = 0.

5x² - 2x - 9 = 0.

General Form of a quadratic equations :
A quadratic equation is an equation of the second degree, meaning it contains at least one term that is squared. The standard form is ax² + bx + c = 0 with a, b, and c being constants, or numerical coefficients, and x is an unknown variable. One absolute rule is that the first constant "a" cannot be a zero.

Nature of the roots :
The nature of roots simply means the category in which the roots are falling upon. The roots may be imaginary, real, unequal or equal. If the discriminate is negative, the roots will be imaginary.

The discriminant determines the nature of the roots of a quadratic equations. The word 'nature' refers to the types of numbers the roots can be — namely real, rational, irrational or imaginary. ... If Δ≥0, the expression under the square root is non-negative and therefore roots are real.

Rational: unequal

Perfect square: irrational

Imaginary: not perfect square


Link of Linear Inequations ( Chapter 4 ) :

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