1. Solving Quadratic Inequations

2. What is to be learned?
The best tactic for solving quadratic inequations

3. Linear Inequations Just like linear equations 3x + 1 = 10 3x = 9 x = 3
(almost)
3x + 1 > 10
3x > 9
x > 3
One big difference

4. 10 > 6
Add 4
>
Multiply by 3
10X3 > 6X3
Divide by 2
10÷2 > 6÷2
Divide by -2
10÷(-2) 6÷(-2)
-5 -3 
If dividing/multiplying by a negative you must turn sign round  
>
<
>  

5. No real roots? 2x2 - 8x + g = 0 c.f. ax2 + bx + c = 0
a = 2, b = -8, c = g
For no real roots
(-8)2 – 4(2)g < 0
64 – 8g < 0
64 < 8g
8 < g
b2 – 4ac < 0
Inequation
-8g < -64 g
>
< -8
g > 8

6. Solving Quadratic Equations
Solve x2 - 2x – 8 = 0
Factorise
(x – 4)(x + 2) = 0
x = 4 or x = -2
Big Nasty Formula
Trial and Error
Try x = 2 22 – 2(2) – 8 = -8 
Try x = 4  42 – 2(4) – 8 = 0 

7. Solving Quadratic Equations
Solve x2 - 2x – 8 = 0
Graphically
y = x2 - 2x – 8
very easy if
x2 - 2x – 8 = 0
you have a graph
x = -2 or 4 -4 -2 2 4

8. Solving Quadratic Inequations
Graphically is the way to go
Solve x2 + 2x – 15 < 0
Need graph
y = x2 + 2x – 15
Find Roots Factorise
(x + 5)(x – 3)
roots x=-5 or 3

9. Solving Quadratic Inequations
Solve x2 + 2x – 15 < 0
Roots x = -5 or 3
x2 + 2x – 15 < 0
y = x2 + 2x – 15
y positive -5 3
y negative

10. Solving Quadratic Inequations
Solve x2 + 2x – 15 < 0
Roots x = -5 or 3
x2 + 2x – 15 < 0
y = x2 + 2x – 15
x is between -5 and 3
-5 < x < 3
y positive -5 3
y negative

11. Solving Quadratic Inequations
Best done by drawing a graph
For graph, need
For roots
roots
Factorise

12. Solve x2 + x – 6 > 0
Need graph
y = x2 + x – 6
Find Roots Factorise
(x + 3)(x – 2)
r oots x= -3 or 2

13. Solving Quadratic Inequations
Solve x2 + x – 6 >0
Roots x = -3 or 2
x2 + x – 6 > 0
y = x2 + x – 6
y positive -3 2
y negative

14. Solving Quadratic Inequations
Solve x2 + x – 6 >0
Roots x = -3 or 2
x2 + x – 6 > 0
x < -3
and x > 2
y = x2 + x – 6
y positive -3 2
y negative