VEDIC MATHS-94

VEDIC MATHS

                           By OMKAR TENDOLKAR

Hello friends,

                      This is  post number 94 from the series of "Vedic maths" blogs. Here in this blog we will learn about "Quadratic Equations-I"

Quadratic Equations:

Here in this post we will learn how to solve quadratic equations using Vedic maths.

Quadratic equations are of the form:

 a(x)^2 + bx + c = 0

Quadratic means ‘two’. So here the unknown variable x will have two values.

Here we have the formula for solving the quadratic equation as:

(-b±√(b²-4ac))/(2a) .

Examples :

1. Here we have our first sum: 7(x)^2 - 5x - 2 = 0

Here a = 7, b = -5 and c = -2.

So we apply the formula (-b±√(b²-4ac))/(2a) 

Here, the differential is the square root of the discriminant.

So we’ll get  ______________

14x - 5 = ± √ 25 - ( 4 × 7 × -2)

14x - 5 = ± (81)^1/2

14x - 5 = ± 9

x =   (9 +5) / 14 = 1.

x = (-9 + 5) / 14 = 2/7.

Answer:

x = 1 & x = 2/7.

2. Here we have our first sum: 6(x)^2 + 5x - 3 = 0

Here a = 6, b = 5 and c = -3.

So we apply the formula (-b±√(b²-4ac))/(2a) 

Here, the differential is the square root of the discriminant.

So we’ll get 

                     ______________

12x + 5 = ± √ 25 - ( 4 × 6 × -3)

12x + 5 = ± (97)^1/2

12x + 5 = ± √(97)

x = [-5 ± √(97)] / 12.

Now, x = [-5 + √(97)]/12, x = [-5 - √(97)]/12. 

Answer:

x = [-5 + √(97)]/12 & x = [-5 - √(97)]/12. 

3. Here we have our first sum: 2(x)^2 - 5x + 2 = 0

Here a = 2, b =-5 and c = -2.

So we apply the formula (-b±√(b²-4ac))/(2a) 

Here, the differential is the square root of the discriminant.

So we’ll get 

                  ______________

4x - 5 = ± √ 25 - ( 4 × 2 × 2)

4x - 5 = ± √(9)

4x - 5 = ± 3

x = [ 5 + 3 ] / 4 = 8/4 = 2.

x = [ 5 - 3 ] / 4  = 2/4 = 1/2.

Answer:

x = 2 & x = 1/2. 

The simplicity of this method can be vouched from examples given above.

You may try following examples.

1. 2(x)^2 -  3x +  5 = 0

2.   (3)^2 + 4x +  3 = 0.

3. (2x)^2 + 3x - 20 = 0.

In next blog we will discuss about "Quadratic Equation-II".     

Are you excited for this?...

Then, please wait for it.

I will post my new blog in next week.

We will meet very soon through our next  blog. Till that stay connected, stay healthy and stay safe.

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Good day😊