CHAPTER 2

Quadratic Expressions and Equations

·  Quadratic expressions in the form ax² + bx + c, where a, b and c are constants, a ≠ 0 and x is an unknown.

·  Quadratic expressions can be formed by multiplying two linear expressions.

( x + a ) ( x + b )

= x² + bx + ax + ab

·  Factorisation of Quadratic Expressions

1. ax² + bx                              3.  x² + bx + c

= x ( ax + b)                           = ( x + m ) (x + n )

Example:                               Example :

3x² + 2x                                  x² + 3x + 2

= x ( 3x + 2)                           = ( x + 1 ) (x + 2 )

2. (ax)² - b²                            4. ax² + bx + c

= ( ax - b) ( ax + b)                = (  px + m ) ( qx + n )         

Example :                              Example :

(2x)² - 1²                                6x² + 5x + 1

= ( 2x - 1) ( 2x + 1)               =(  3x + 1 ) ( 2x + 1)

We can also use the cross method to factorise quadratic expressions in the form of x² + bx + c and ax² + bx + c

Try this using the method :

How about this ? Can you use the same method ?

·  Roots of Quadratic Equations

Finding the roots of a quadratic equation.

ax² + bx + c = 0 ( General Form )

(  px + m ) ( qx + n ) = 0 ( Factorisation )

px + m = 0             qx + n = 0

         x = - m                x  = - n  

                   p                             q