**QUADRATIC EXPRESSION:** If are complex numbers then is called a quadratic expression in x.

**QUADRATIC EQUATION:** If

are complex numbers then

is called a quadratic equation in x.

**ROOT OF A QUADRATIC EQUATION:** If

then

is a root or solution of the quadratic equation

A quadratic equation can not have more than two roots or two solutions. The roots of are and its discrminent is .

**NATURE OF THE ROOTS OF THE EQUATION **
1.If a,b,c are real and , then the roots are real and distinct.

2.If a,b,c are real and , then the roots are real and equal.

3.If a,b,c are real and , then the roots are two conjugate complex numbers.

4.If a,b,c are rational and , and is a perfect square then the roots are rational and distinct.

5.If a,b,c are rational and , and is not a perfect square then the roots are conjugate surds i.e .

6.If a,b,c are rational and , then the roots are conjugate complex numbers i.e, .

**FORMATION OF THE QUADRATIC EQUATION WITH ROOTS AND :** The quadratic equation whose roots are

and

is

.

**RELATION BETWEEN THE ROOTS OF **
1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

For rest go to CAT India Online’s CATclub

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