1 Press Ctrl-A ©G Dear2008 – Not to be sold/Free to use The Descriminant Stage 6 - Year 11 Mathematic (Preliminary)

2  = b 2 – 4ac This is part of the quadratic roots formula! x = -b + b 2 – 4ac 2a Note: Roots and Solutions can be used interchangeably. The Discriminant

3  > 0  Two Real Solutions  = 0  One Real Solution  < 0  No Real Solutions There are three possibilities for  The Discriminant

4  > 0  Two Real Solutions a > 0 a < 0 The Discriminant

5  = 0  One Real Solution a > 0 a < 0 The Discriminant

6  < 0  No Real Solutions a > 0 a < 0 The Discriminant

7  - a perfect square (e.g. 9=3 2 )   - a NOT perfect square (e.g. 8)  The roots/solutions are Rational The roots/solutions are Irrational The Discriminant

8  > 0  Two Real Solutions x 2 + 5x - 6 = 0  = x 1 x -6  = = 49 (Perfect Square) Therefore Two Rational Roots The Discriminant

9  > 0  Two Real Solutions x 2 + 5x - 4 = 0  = x 1 x -4  = = 41 (Not Perfect Square) Therefore Two Irrational Roots The Discriminant

10  = 0  One Real Solution x 2 - 6x + 9 = 0  = (-6) 2 – 4 x 1 x 9  = = 0 (Perfect Square???) Therefore One Rational Root The Discriminant

11  < 0  No Real Solutions x 2 + x + 1 = 0  = 1 2 – 4 x 1 x 1  = = -3 Therefore No Roots (Will save a lot of grief trying to solve it!) The Discriminant

12  > 0  Two Real Solutions  = 0  One Real Solution  < 0  No Real Solutions There are three possibilities for  The Discriminant