**Quadratic Equation definition**: A quadratic equation in x is an equation that can be written in the form of

a\;x^2-bx+c=0\;\;\;\;\;\;\;\;\;\;\;\;\;;a,\;b,\;c are real numbers and a ≠ 0.

Another name for a quadratic equation in x is **2nd Degree Polynomial** in x.

**Quadratic Equation** **Examples:** The following equations are the quadratic equations:

- x^2-7x+9=0\;\;\;\;\;\;\;\;\;\;\;\;\;;a=1,\;b=-7,\;c=9
- 5x^2+8x-9=0\;\;\;\;\;\;\;\;\;\;\;\;\;;a=5,\;b=8,\;c=-9
- -7 x^2-9x-8=0\;\;\;\;\;\;\;\;\;\;\;\;\;;a=-7,\;b=-9,\;c=-8

**Solution of Quadratic Equations:**

- There are three basic techniques for solving a quadratic equation:
**By Factorization.****By Completing Squares, extracting square roots.****By applying the Quadratic formula**.

**By Factorization:** It involves factoring the polynomial

a\;x^2-bx+c=0\;\;\;\;\;\;\;\;\;\;\;\;\;;a,\;b,\;c are real numbers and a ≠ 0.

It makes use of the fact that if xy = 0, then x = 0 or y = 0.**For Example**:

If (x - 2) (x - 4) = 0, then either x - 2 = 0 or x - 4 = 0

**Example 1**: Solve the equation x^2-7x+10=0 by factorization.**Solution:**

x^2-7x+10=0 .

⇒x^2-5x-2x+10=0

⇒x(x-5)-2(x-5)=0

⇒ (x - 2) (x - 5) = 0.

∴ either x - 2 = 0 ⇒ x = 2

or x - 5 = 0 ⇒ x = 5

∴ the given equation has two solutions: 2 and 5

so **Solution set = {2,5}**