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The DescriminantThe DescriminantStage 6 - Year 11Stage 6 - Year 11

Mathematic(Preliminary)

2

= b2 – 4ac

This is part of the quadratic roots formula!

x = -b + b2 – 4ac2a

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=32)

- a NOT perfect square (e.g. 8)

The roots/solutions are Rational

The roots/solutions are Irrational

The Discriminant

8

> 0 Two Real Solutions

x2 + 5x - 6 = 0

= 52 - 4 x 1 x -6

= 25 + 24 = 49 (Perfect Square)

Therefore Two Rational Roots

The Discriminant

9

> 0 Two Real Solutions

x2 + 5x - 4 = 0

= 52 - 4 x 1 x -4

= 25 + 16 = 41 (Not Perfect Square)

Therefore Two Irrational Roots

The Discriminant

10

= 0 One Real Solution

x2 - 6x + 9 = 0

= (-6)2 – 4 x 1 x 9

= 36 - 36 = 0 (Perfect Square???)

Therefore One Rational Root

The Discriminant

11

< 0 No Real Solutions

x2 + x + 1 = 0

= 12 – 4 x 1 x 1

= 1 - 4 = -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