# Derivation of Formula

## Derivation of Sum of Arithmetic Progression

**Arithmetic Progression, AP**

Definition

*d*.

Examples of arithmetic progression are:

- 2, 5, 8, 11,... common difference = 3
- 23, 19, 15, 11,... common difference = -4

- Read more about Derivation of Sum of Arithmetic Progression
- Log in or register to post comments
- 56332 reads

## Derivation of Pythagorean Theorem

**Pythagorean Theorem**

In any right triangle, the sum of the square of the two perpendicular sides is equal to the square of the longest side. For a right triangle with legs measures $a$ and $b$ and length of hypotenuse $c$, the theorem can be expressed in the form

- Read more about Derivation of Pythagorean Theorem
- Log in or register to post comments
- 28639 reads

## Sum and Product of Roots

The quadratic formula

give the roots of a quadratic equation which may be real or imaginary. The ± sign in the radical indicates that

where x_{1} and x_{2} are the roots of the quadratic equation ax^{2} + bx + c = 0. The sum of roots x_{1} + x_{2} and the product of roots x_{1}·x_{2} are common to problems involving quadratic equation.

- Read more about Sum and Product of Roots
- Log in or register to post comments
- 16709 reads

## Derivation of Quadratic Formula

The roots of a quadratic equation *ax*^{2} + *bx* + *c* = 0 is given by the quadratic formula

The derivation of this formula can be outlined as follows:

- Divide both sides of the equation
*ax*^{2}+*bx*+*c*= 0 by*a*. - Transpose the quantity
*c*/*a*to the right side of the equation. - Complete the square by adding
*b*^{2}/ 4*a*^{2}to both sides of the equation. - Factor the left side and combine the right side.
- Extract the square-root of both sides of the equation.
- Solve for
*x*by transporting the quantity*b*/ 2*a*to the right side of the equation. - Combine the right side of the equation to get the quadratic formula.

See the derivation below.

- Read more about Derivation of Quadratic Formula
- Log in or register to post comments
- 52599 reads

## Pages

- « first
- ‹ previous
- 1
- 2
- 3