Solving Quadratic Equations by Extracting Square Roots

Mathematics Grade 9

1. Solving Quadratic Equations by Extracting Square Roots

2. RATIONAL NUMBERS Definition : Any number that can be written as a fraction p/q, where p and q are integers and q is not zero. Examples : 1/2, -3/4, 0.75 (which is 3/4), 0, 5 (which is 5/1).

3. Irrational Numbers: Definition : Numbers that cannot be expressed as a simple fraction (p/q) where p and q are integers and q is not zero. Examples : √2, √3, π (pi), e ( Euler's number ), i ( imaginary number )

4. Solving Quadratic Equations by Extracting Square Roots Quadratic equations that can be written in the form x 2 = k can be solved by applying the following properties:

5. Example 1: Find the solutions of the equation x 2 – 16 = 0 by extracting square roots. Example 2: Solve the equation t 2 = 0 . Example 3: Find the roots of the equation s 2 + 9 = 0 . Example 4: Find the solutions of the equation (x – 4) 2 – 25 = 0 .