Problems Leading to Quadratic Equations

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Presentation transcript:

Problems Leading to Quadratic Equations

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.

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.

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

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.