Surds and Quadratics

AS 91577

Surds

• Adding

• Subtracting

• Multiplying

• Dividing

Adding and subtracting surds

Multiplying SurdsExample 1:

Multiplying SurdsExample 2:

Dividing surds(Rationalising)

Example 1

Multiply top and bottom by

Dividing surds(Rationalising)

Example 2

Multiply top and bottom by

Recognising terms

Worksheet 1

Quadratics

General formula:

Example 1.

Solving for the roots (i.e. y = 0)

Method 1: Factorising

Method 2: Quadratic Formula

Method 3: Graphics Calculator

•Equation Mode

•F2: Polynomial

•Degree: 2 (F1)

•Enter 1, -2, -3

•Solve (F1)

Equation has 2 real solutionsx = 3, -1

Example 2

Method 1: Factorize

Method 2: Quadratic Formula

Equation has two equal solutions:x = 3

Example 3

Equation cannot be factorised.

Using quadratic formula

We use the substitution

A complex number

Equation has 2 complex solutions

Real part Imaginary Part

Note: Because the coefficients are real, solutions come in

conjugate pairs i.e.

Equation has 2 imaginary solutions.

Forming quadratic equations from 2 solutions.

If solutions are

Example 1

Quadratic equation is

Example 2

Quadratic equation is

Example 3

Worksheet 2