1. SOLVING QUADRATIC EQUATIONS BY FACTORISATION

2. This very important result is used for solving quadratic equations. If a × b = 0thena = 0orb = 0

3. 1 Solve factorise check:0 2 – 3 × 0 = 0 3 2 – 3 × 3 = 0

4. 2 Solve factorise check:0 2 + 5 × 0 = 0 (−5) 2 + 5 × (−5) = 0

5. 3 Solve factorise check:2 2 − 5 × 2 + 6 = 0 3 2 − 5 × 3 + 6 = 0

6. 4 Solve factorise check:(−7) 2 + 5 × (−7) − 14 = 0 (2) 2 + 5 × 2 − 14 = 0

7. 5 Solve factorise check:2 × (½) 2 + 5 × (½) − 3 = 0 2 ×(−3) 2 + 5 × (−3) − 3 = 0

8. Problems involving quadratic equations

9. 1 The two rectangles have the same area. Find x. factorise x + 1 x + 3 x 2x + 2 x must be positive, so x = 3 4 6 3 8 area = 24 area = 24 check:

10. 2 The triangle is right-angled. Find x. factorise x − 1 2x2x 2x + 1 x must be positive, so x = 6 using Pythagoras 12 5 13 check: