**Quadratic Equation class 10**

__Quadratic Polynomial, Quadratic Equation and Solution of Quadratic Equation__

__(Discriminant of Quadratic Equation and Relation between Roots of the Quadratic Equation)__

The Standard form or General Form of Quadratic Polynomial is **ax ^{2} + bx + c**, where a, b and c are constants and x is the variable.

The Standard Form or General Form of Quadratic Equation is

**ax ^{2} + bx + c = 0**

where **a, b** and **c** are constants and x is the variable.

The values of **x** which satisfies the Quadratic Equation are called its solutions or roots. A Quadratic Equation has **two distinct roots** or **two equal roots**. The roots of the equations may be **Real Roots** representing ** real numbers** as well as

**Imaginary Roots**representing

**.**

*Complex Numbers*__Derivation of Roots of Quadratic Equation__

__Derivation of Roots of Quadratic Equation__

__Sum and Products of roots of Quadratic Equation__

__Sum and Products of roots of Quadratic Equation__

### The roots of the Quadratic Equation are ax^{2} + bx + c = 0 are

Now, sum of roots is

#### Quadratic equation class 10:- Hence the sum of the roots of the quadratic equation ax^{2} + bx + c = 0 is

Again, the roots of the Quadratic Equation are ax^{2} + bx + c = 0 are

### Basic Proportionality Theorem or Thales Theorem

Now, Product of roots is

Hence the products of the roots of the quadratic equation ax^{2} + bx + c = 0

Once again, we have, the Standard Form or General Form of Quadratic Equation is

ax^{2} + bx + c = 0

Dividing both sides by a, we get

The Quantity b^{2} – 4ac is called the **Discriminant***of the Quadratic Equation *ax^{2} + bx + c = 0 *and it is denoted by D.*

**D = ****b ^{2} – 4ac**

- If
D ≥ 0, then the Quadratic Equation has two real roots.**Discriminant**

(I) If * Discriminant* D > 0, the Quadratic Equation has

**.**

__two Distinct Real Roots__(II) If * Discriminant* D = 0, the Quadratic Equation has

**.**

__two Equal Real Roots__**Math Quadratic equation class 10**

2. If * Discriminant* D < 0, the Quadratic Equation has

**. It has**

__NO Real Roots__**Imaginary Roots**representing

**Complex Numbers**.

### National Mathematics Day of India –राष्ट्रीय गणित दिवस

Great work, Guruji