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