Vedic Maths Linear, Quadratic and Cubic Polynomials

Vedic Mathematics offers various techniques to handle different types of polynomials. Here are some Vedic Math techniques and principles that can help with linear, quadratic, and cubic polynomials:

Linear Polynomials

For solving linear equations of the form ax+b=0:

1. Simple Transposition:

Solve for x by isolating it on one side of the equation.

Example: 2x + 3=0 implies x=− 3 / 2

Quadratic Polynomials

For solving quadratic equations of the form ax²+bx+c=0 , Vedic Mathematics offers the following techniques:

1. Sutra Method:

Factorize the quadratic equation if possible.

Use the "Vertically and Crosswise" method to solve quadratic equations by breaking them into simpler parts.

Example: Solve x²+5x+6=0 by factoring into (x+2)(x+3)=0, so x=−2 and x=−3.

2. Completing the Square:

Rearrange the equation to complete the square and solve.

Example: x²+4x+4=(x+2)² , so x = -2

Cubic Polynomials

For solving cubic equations of the form ax³ + bx² + cx + d =0:

1. Factorization:

Factor the cubic polynomial if possible.

Example: Solve x³ - 6x² + 11x - 6 = 0 by factoring into (x−1)(x−2)(x−3)=0, so x=1,2,3.

2. Vedic Sutras:

Use specific Vedic sutras for more complex cubic equations, which may involve breaking down the equation using various Vedic methods like the "Paravartya Yojayet" sutra for substitution and simplification.

Practise it: quick arithmetic makes factoring easier, so warm up with one of our free math games.