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Quadratic Equations

 

As calculus is an integral part of Vedic mathematics, differential calculus is made use of in Vedic sutras for solving quadratic equations by breaking them into two simple equations.

Accordingly it has been stated in the Vedas that the first differential of the quadratic equation is equal to square root of the discriminant.

The discriminant is given as the square of coefficient of 'x' minus the product of double the coefficient of x2 and double the independent term.

Example :

 Consider    x2 + 4x - 3 = 0

Then its first differential is  2x + 4

Its discriminant is  42 - 2 * 1 * 2 * (-3) = 28

Therefore according to the sutra     

                      2x + 4 = (28)-2  =  2(7)-2         

                       ==> x = 2 (7)-2


There are some more sutras and methods which when applied to quadratic equations in special cases make the job easier. Given below are a few types (methods).

Reciprocals
Using shoonyam samucchaye sutra
Using shoonyam samucchaye and shoonyam anyat sutras