## 2.2 Factorisation of Quadratic Expression

2.2 Factorisation of Quadratic Expression   (A) Factorisation quadratic expressions of the form    ax2 + bx + c, b = 0 or c = 0 1. Factorisation of quadratic expressions is a process of finding two linear expressions whose product is the same as the quadratic expression. 2. Quadratic expressions ax2 + c and ax2 … Read more2.2 Factorisation of Quadratic Expression

## 2.5 Quadratic Equations, SPM Paper 2 (Long Questions)

Question 9:Solve the following quadratic equation:4x (x + 4) = 9 + 16xSolution: 4x( x+4 )=9+16x 4 x 2 +16x=9+16x    4 x 2 −9=0 ( 2x ) 2 − 3 2 =0 ( 2x+3 )( 2x−3 )=0 2x+3=0     or     2x−3=0      2x=−3                2x=3        x=− 3 2                  x= 3 2     Question 10:Solve the following quadratic equation:(x + 2)2 = … Read more2.5 Quadratic Equations, SPM Paper 2 (Long Questions)

(A) Identifying quadratic expression 1. A quadratic expression is an algebraic expression of the form ax2 + bx + c, where a, b and c are constants, a ≠ 0 and x is an unknown. (a) The highest power of x is 2. (b) For example, 5×2– 6x + 3 is a quadratic expression. Example 1 State whether … Read more2.1 Quadratic Expressions

2.3 Quadratic Equations 1. Quadratic equations are equations which fulfill the following characteristics: (a) Have an equal ‘=’ sign (b) Contain only one unknown (c) Highest power of the unknown is 2.   For example,   2. The general form of a quadratic equation is written as: (a) ax2 + bx + c = 0, where a ≠ 0, b ≠ … Read more2.3 Quadratic Equations

## 2.1 Quadratic Expression (Sample Questions)

Example 1: Form a quadratic expression by multiplying each of the following. (a) (6p – 2)(2p – 1) (b)   (m + 5)(4 – 7m) (c)    (x + 2) (2x – 3) Solution: (a) (6p – 2)(2p – 1) = (6p)(2p) + (6p)(-1) + (-2)(2p) +(-2)(-1) = 12p2 – 6p – 4p + 2 = 12p2 – … Read more2.1 Quadratic Expression (Sample Questions)

## Roots of Quadratic Equation Example 3 & 4

Example 3 Solve the quadratic equation 5 x 2 =3(x+2)−4. Solution: 5 x 2 =3(x+2)−4 5 x 2 =3x+6−4 5 x 2 −3x−2=0 ( 5x+2 )( x−1 )=0 5x+2=0       or     x−1=0        x=− 2 5                  x=1 Example 4 Solve the quadratic equation  3x(x−3) 4 =−x+3. Solution: 3x(x−3) 4 =−x+3 3 x 2 −9x=−4x+12 3 x 2 −5x−12=0 ( 3x+4 )( x−3 )=0 3x+4=0       or     x−3=0        x=− 4 3                  x=3

## 2.4 Roots of Quadratic Equations

2.4 Roots of Quadratic Equations 1. A root of quadratic equation is the value of the unknown which satisfies the quadratic equation. 2. Roots of an equation are also called the solution of an equation. 3. To solve a quadratic equation by the factorisation method, follow the steps below: Step 1: Express the quadratic equation in general form ax2 … Read more2.4 Roots of Quadratic Equations