Sreedhar acharya s formula 1

We will discuss here about the methods of solving quadratic equations.

The quadratic equations of the form ax\(^{2}\) + bx + c = 0 is solved by any one of the following two methods (a) by factorization and (b) by formula.

(a) By factorization method:

In order to solve the quadratic equation ax\(^{2}\) + bx + c = 0, follow these steps:

Step I: Factorize ax\(^{2}\) + bx + c in linear factors by breaking the middle term or by completing square.

Step II: Equate each factor to zero to get two linear equations (using zero-product rule).

Step III: Solve the two linear equations.

This gives two roots (solutions) of the quadratic equation.

Quadratic equation in general form is

ax\(^{2}\) + bx + c = 0, (where a ≠  0) ………………… (i)

Multiplying both sides of, ( i) by 4a,

4a\(^{2}\)x\(^{2}\) + 4abx + 4ac = 0

⟹ (2ax)\(^{2}\) + 2 .

2ax . b + b\(^{2}\) + 4ac - b\(^{2}\) = 0

⟹ (2ax + b)\(^{2}\) = b\(^{2}\) - 4ac [on sim