COMPLETING SQUARE | SOLVE QUADRATIC EQUATIONS BY COMPLETING SQUARE | 10TH CLASS MATHEMATICS

SOLUTION OF QUADRATIC EQUATIONS BY COMPLETING SQUARE METHOD EXPLAINED IN URDU/HINDI 10TH CLASS MATHEMATICS

SOLUTION OF QUADRATIC EQUATIONS BY COMPLETING SQUARE:

·         In this method here are a few steps to follow:

i)                    First of all make the coefficient of x² ‘1’.

ii)                  Take the constant ‘c’ to the right hand side of the quadratic equation.

iii)                Now multiply the coefficient of ‘x’ by ‘1/2’ and then square.

iv)                Add that squared term to the both sides of the equation.

v)                  Simplify the equation as much as possible.

vi)                Take square root of the both sides of equation.

vii)              Simplify to possible extent and find values of variable.

viii)            Write solution set.

Example:-        Solve the equation by completing square method.

                        x² – 3x – 4 = 0

Firstly, we have to make coefficient of x² ‘1’ which is already ‘1’.

Now, take the constant term to the right hand side of the equation.

                        x² – 3x = 4

In this step, we are to multiply coefficient of ‘x’ b by ‘1/2’.

As we know     a = 1, b = -3, c = -4

So,       b x 1/2 = -3 x 1/2 = -3/2 

Squaring,         (-3/2)²  and then adding (-3/2)² to the both sides of the equation.

                        

                          x²  - 3x + (-3/2)²  = 4 + (-3/2)²

Here we see that on the L.H.S of the equation, a complete square is being formed .

As we know (a – b)² = a² – 2ab + b² , so by this formula, we see the above equation forming a complete square on the left side.

Therefore,        (x – 3/2)²          =          4 + 9/4

                      

                          (x – 3/2)²          =          16 + 9 /4

                        √

                          (x – 3/2)²       =          ± √25/4

                        

                         (x – 3/2)           =          ±5/2

or                                 x          =          3/2 ± 5/2

Here two possibilities may arise, we take either +5/2 or -5/2

So,       x = 3/2 + 5/2                            or                     x = 3/2 – 5/2

x = 8/2 & x = 4                                                or                     x = -2/2 & x = -1\

Therefore, solution set is {-1, 4}

                                                           

For understanding more comprehensively, watch the video from start to end and full procedure of solving the Quadratic Equations by completing square has been explained with many examples.

Here is the video lecture explaining solution of quadratic equations in Urdu/Hindi in the most easy and efficient way. In this video you’ll learn how to solve quadratic equations by the completing square method? You'll also learn the way to solve quadratic equations by completing square step by step with examples in easy wording. You’ll learn this method to solve quadratic equations in the most efficient way. If there's still any confusion regarding this video lecture, you can comment or contact us directly through social links provided so your comments will be entertained gladly. Get everything related to study and academic content through this channel and blog for useful and important notes and materials.

Thanks for visiting blog, also visit my YouTube Channel for more informative and useful videos and lectures.

Read More

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.

 Thanks for visiting blog, also visit my youtube channel for more informative and useful videos and lectures. 

Read More