Quadratic equation

 Quadratic equation 

•A polynomial equation of degree two is called a quadratic equation.

• General form of a quadratic equation (variable is x ) is: 

• A few examples of Quadratic equation are as follows: 

2x^2 +3x=0

x^2+1=0

3x^2=0.

• Solution of a quadratic equation : 

A quadratic equation can be solved in the following way: 

By factorising: 

Quadratic equation 

This formula is known as Shreedhar Acharya formula.

• Discriminant: 

The term : (b^2-4ac)  is known as discriminant of the quadratic equation. It determines the nature of roots of the Quadratic equation.

* If the discriminant of the quadratic equation is zero, the quadratic equation has real and equal roots. 

* If the discriminant is greater than zero , the quadratic equation has real and distinct roots.

* If the discriminant is less than zero, the quadratic equation has imaginary roots.

• Relation between roots and coefficients: 

If p and q are two roots of the Quadratic equation, then: 

p+q= (-b/a)       and    pq= (c/a).

That means: