30MSC 2023 #27: Vedic Methods of Solving Quadratic Equations.

When a quadratic equation cannot be easily factored, a technique called completing the square is used. However, this method is tedious and difficult for most students.

The quadratic formula,  which is derived by completing the square, is often used instead.

But many students find it hard to memorize the quadratic formula. In Vedic Math, there is an easy word formula to solve quadratics: The differential is equal to the square root of the discriminant.

For a 2nd degree equation expressed in standard form, ax^2 + bx + c = 0, the differential is 2ax + b and the discriminant is b^2 – 4ac. We can see that that Vedic 2ax + b = sqrt (b^2 – 4ac)  isa more “user-friendly” form of the quadratic formula.

The above mentioned word formula is used to directly answer the featured example for today which was taken in the Seniors questionnaire of the 4th Philippine National Vedic Mathematics Olympiad:Which of the following equations has the same solution set as  2x^2 – x = 6?

The given equation is standard form is 2x^2 – x – 6. Here a = 2; b = -1 and c = -6. Therefore,  we have     4x – 1= sqrt [ -1^2 – 4(2)(-6)]

Or 4x – 1 = sqrt ( 1+ 48) = ± 7

Other Vedic methods of solving quadratic equations are presented in Chapter 7 of our forthcoming book, 30 Master Strategies of Computing, Vol III.

Follow us on our Facebook page, MATH-Inic Philippines at https://www.facebook.com/MATHInicPhils to see tomorrow’s 30MSC 2023 #28: Specific and General.