INTRODUCTION TO QUADRATIC EQUATIONS | 10th CLASS MATHEMATICS

Introduction to Quadratic Equations in Urdu/Hindi Chapter 1/ 10th Class Mathematics 

• QUADRATIC EQUATIONS

• Definition:- An equation which contains the square of unknown (variable) but no higher power is called a Quadratic Equation or an Equation of Second Degree.

• Standard Form:- If we have a variable ‘x’ the standard form of a quadratic equation is

                                               

ax² + bx + c = 0          a≠0      ……………… (A)

In the above equation, a, b & c are some real numbers. ‘a’ is called coefficient of ‘x²’ , ‘b’ is called coefficient of ‘x’ and ‘c’ is called a constant.

In equation (A), it is given that ‘a’ must not be equal to zero. If we take a = 0, then the equation will be no longer a quadratic equation but a linear equation. So it is necessary to mention that ‘a’ must not be equal to zero. Although a may have negative value as well as positive value.

If a = 0, then               

(0)x² + bx + c = 0

                                    0     +   bx + c = 0

                                                bx + c = 0        (A linear equation)

So,       6x² + 4x - 3 = 0 & -3x² + 5x + 2 = 0 are two quadratic equations. Also x² + 9x = 20 is a quadratic equation but not in the standard form.

• Pure Quadratic Equation:- In a quadratic equation, if we put b = 0, then the equation reduces as

                                   

ax² + (0)x + c = 0

                                    ax² +    0   + c = 0

                                               ax²  + c = 0       (A pure quadratic equation)

Thus, 3x² + 9 = 0 & 5x² = 30 are pure quadratic equations.

• From the all above mentioned equations, we can find out the constants a, b & c by comparing these equations with the standard form equation (A).

• Variable:- A variable is allotted for some specific numeric value and is unknown or changeable. As from its name, it is oriented from the word ‘vary’ which means ‘change’. So variable means ‘changeable.’ It has no fixed or constant value, with time those values may change. Just for instance, if we have a variable ‘x’ in an equation, it may have some specific value but we cannot say that this value is specified to ‘x’ forever. It has some value in this equation and may have some different value in the other. Therefore, a variable does not have a fixed numeric value.
• Constant:- On the other hand, a constant is specified for a fixed numeric value. Its value does not change with the passage of time. For example, '5' is five today and will be '5' tomorrow. It'll not change its value with time. Also the speed of light is represented by 'c' and c = 3x10⁸ms^-1.  Thus this 'c' is a constant having constant value which would never be changed anywhere and anytime. Therefore, a constant has a fixed numeric value.

Here is the video lecture explaining quadratic equations in Urdu/Hindi in the most easy and efficient way. In this video you'll get to know a brief introduction of Quadratic Equations in Urdu/Hindi. You'll be able to know what the quadratic equations actually are and how to recognize these equations? Which parameters are used in quadratic equations? What are necessary conditions for equations to be quadratic ones? What is the standard form of quadratic equations? Here's all you get in this lecture. Get everything related to study and academic content through this channel and blog for useful and important notes and materials.

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