1. Problems Leading to Quadratic Equations

2. I have learnt different methods of solving quadratic equations.
How to use these methods to solve practical problems leading to quadratic equations?
I have learnt different methods of solving quadratic equations.
1. Factor method
2. Quadratic formula
3. Graphical method
Let’s see the following example.

3. The sum of a positive number and its square is 72. Find the number.
Let x be the number.
 Step 1: Identify the unknown quantity and use a letter, say x, to represent it.
∴ x + x2 = 72
 Step 2: Form a quadratic equation according to the given conditions.
x2 + x – 72 = 0
(x – 8)(x + 9) = 0
 Step 3: Solve the equation using the factor method.
x – 8 = 0 or x + 9 = 0
x = 8 or x = –9
(rejected)
 Step 4: Check whether the solutions are reasonable.
x must be positive
∴ The number is 8.

4. Follow-up question
Mr Chan is 30 years older than his daughter. The product of their ages is 675. Find the age of Mr Chan.
Let x be the age of Mr Chan,
then x – 30 is the age of his daughter.
 Represent the other unknown quantity in terms of x.
∴ x(x – 30) = 675
x2 – 30x – 675 = 0

5. By the quadratic formula
Follow-up question
Mr Chan is 30 years older than his daughter. The product of their ages is 675. Find the age of Mr Chan.
By the quadratic formula
 The age must be positive.
∴ Mr Chan is 45 years old.