Edexcel IGCSE Maths 复习笔记 2.16.2 Solving Inequalities - Quadratic
Edexcel IGCSE Maths 复习笔记 2.16.2 Solving Inequalities - Quadratic
What is a quadratic inequality?
- An?Inequality?tells you that one expression is greater than (“>”) or less than (“<”) another
- “?” means “greater than or equal to”
- “?” means “less than or equal to”
- A?Quadratic Inequality?has an?x2?(or a?y2?etc) in it
- For example, 3x2?+ 4x ? 7 would be read “3x2?+ 4x is?greater than or equal to?7”
Solving quadratic inequalities
- Solving quadratic inequalities requires you to be able to factorise quadratics so you might want to have a look at those notes first
- You also need to know how to?SKETCH?graphs and use?Number Lines
- REARRANGE?so that your “quadratic >0” (or <0)
- FACTORISE?the quadratic
- SKETCH?a graph of the quadratic
- Use x-axis as a?NUMBER LINE?to show where the graph is above (if ≥ or >) or below (if ≤ or <) the x-axis
- Turn the number line into a?PAIR?of inequalities or a?DOUBLE?inequality
Exam Tip
- When dealing with quadratic inequalities always make sure that you end up with a positive number in front of the x2
- For example, to solve the inequality 4 - 2x2?> 5x start by adding the 2x2?to (and subtracting 4 from both sides to get 0 > 2x2?+ 5x -4) rather than subtracting the 5x (and getting 4 - 5x -2x2?> 0)
- Why? Because it’s much easier to factorise a quadratic when the coefficient of x2?is positive
Worked Example
Worked Example
Worked Example
Worked Example
Worked Example
Worked Example
Worked Example
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