The document discusses quadratic equations and their properties over multiple years from 2005 to 2008. It provides example quadratic equations and asks the reader to find their roots, determine if they have equal roots, express constants in terms of other variables, and solve the equations. Specifically, it asks the reader to: 1) Find the value of p given one root of an equation. 2) Solve example quadratic equations and express a constant h in terms of k. 3) Determine possible values of p if an equation has two equal roots. 4) Solve another example quadratic equation to three decimal places. The answers provided are: p = 5, x = 1/3 or x = -2, p = 8 or p

1. 2008 2007 2006 2005 TOPIC QUADRATIC EQUATIONS LEARNING OBJECTIVES Understand the concept of quadratic equations and their roots Understand and use the conditions for quadratic equations to have a)two different roots b)two equal roots c)no roots

2. 2008 Answers 3marks It is given that -1 is one of the roots of the quadratic equation x 2 – 4x – p = 0 . Find the value of p.

3. 2007 Answers 4 marks a)Solve the following quadtaic equation; 3x 2 + 5x – 2 = 0 b)The quadratics equation hx 2 + kx + 3 = 0 , where h and k are constants , has two equal roots. Express h in terms of k.

4. 2006 Answers A quadratic equation x 2 + px + 9 = 2x has two equal roots . Find the possible values of p 3 marks

5. 2005 Answers 3 marks Solve the quadratic equations x(2x-5) = 2x -1 Give your answer correct to three decimel places.

6. 2008 p = 5

7. 2007 X = 1/3 or x= -2 b)

8. 2006 P = 8 or P = -4

9. 2005 X= 3.351 or X= 0.1492