- An equation is a statement of equality between two expressions which is not true for all values of the variable involved.
- A polynomial in which maximum power of variable is two is called quadratic equation. General form of quadratic equation is where a, b and c are real numbers and x is a variable and a ≠ 0.

## Roots of a Quadratic Equation:

- The values of variable which satisfies the quadratic equation is called solution of the quadratic equation or the roots of the equation.

whereis called discriminant of the quadratic equation and it is represented by D.

## Solution of a Quadratic Equation:

### (i) By Factorisation Method:

if the factors of the given equation is such that

(dx + e) (fx + g), d≠0, f≠0

### (ii) By Shreedharacharaya formula:

The following formula could be used for equation :

If roots of the quadratic equation is α , β , then

D = , the following table will be helpful to find the nature of roots of a quadratic equation:

Also, if roots of the quadratic equation is α, β, then

Sum of roots, and product of roots,

If roots of the quadratic equation is α , β , then

## Nature of Roots of Quadratic Equation :

The nature of roots of the quadratic equations are dependent upon the discriminantD = , the following table will be helpful to find the nature of roots of a quadratic equation:

Also, if roots of the quadratic equation is α, β, then

Sum of roots, and product of roots,

## Problem Solving Tricks :

- If α and β are the given roots of the quadratic equation , then you can form the equation as;

- If the term containing x and constant term are both zero simultaneously, then both roots of the equation are zero.
- If coefficient of and constant term are equal , then both the roots of equation are reciprocal of each other.
- If there is no term containing coefficient of x, then both the roots of the equation are equal in magnitude but opposite in sign.
- If b is of opposite sign as compared to a and c , then both roots are positive.
- If a, b ,c are all of the same sign, then both the roots are negative.
- If a and c are of opposite signs, then both the roots of the equation are of opposite sign.

## Symmetrical Functions of Root :

**Good Luck!**