Quadratic Inequalities (Edexcel A Level Maths) : Revision Note

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Quadratic Inequalities

Quadratic inequalities

  • Similar to quadratic equations quadratic inequalities just mean there is a range of values that satisfy the solution

  • Sketching a quadratic graph is essential

Can involve the discriminant or applications in mechanics and statistic

2.4.2 Quadratic Inequalities Notes Diagram 1, Edexcel A Level Maths: Pure revision notes

 

How do I solve quadratic inequalities?

  • STEP 1: Rearrange the inequality into quadratic form with a positive squared term

    • ax2 + bx + c > 0 (>, <, ≤ or ≥)

  • STEP 2: Find the roots of the quadratic equation

    • Solve ax2 + bx + = 0 to get x1 and xwhere x1 < x2

  • STEP 3: Sketch a graph of the quadratic and label the roots

    • As the squared term is positive it will be "U" shaped

  • STEP 4: Identify the region that satisfies the inequality

    • For ax2 + bx + c > 0 you want the region above the x-axis

      • The solution is x1 or x > x2 

    • For ax2 + bx + c < 0 you want the region below the x-axis

      • The solution is x > x1 and x < x2  

      • This is more commonly written as x1 < x < x2

  • avoid multiplying or dividing by a negative number

    if unavoidable, “flip” the inequality sign so <>, , etc

    • avoid multiplying or dividing by a variable (x) that could be negative

      (multiplying or dividing by x2 guarantees positivity (unless x could be 0) but this can create extra, invalid solutions)

    • do rearrange to make the x2 term positiveBe careful:

 

2.4.2 Quadratic Inequalities Notes Diagram 3, Edexcel A Level Maths: Pure revision notes

Solving quadratic inequalities on a calculator

  • Be aware of unconventional ways calculators can display an answer

    eg        8 > x > 2 rather than 2 < x < 8

2.4.2 Quadratic Inequalities Notes Diagram 4, Edexcel A Level Maths: Pure revision notes

Examiner Tips and Tricks

  • A calculator can be super-efficient but some marks are for method.

  • Use your judgement:

  • is it a “show that” or “prove” question?

    • how many marks?

    • how long is the question?

Worked Example

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Paul

Author: Paul

Expertise: Maths Content Creator (Previous)

Paul has taught mathematics for 20 years and has been an examiner for Edexcel for over a decade. GCSE, A level, pure, mechanics, statistics, discrete – if it’s in a Maths exam, Paul will know about it. Paul is a passionate fan of clear and colourful notes with fascinating diagrams.

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