Solving Quadratic Inequalities (OCR GCSE Maths) : Revision Note

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Solving Quadratic Inequalities

What are 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

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 positive. Be careful:

 

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

Examiner Tips and Tricks

  • Always start by rearranging to a quadratic with positive squared term

  • Always sketch a graph of the quadratic before deciding the final answer

Worked Example

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Amber

Author: Amber

Expertise: Maths Content Creator

Amber gained a first class degree in Mathematics & Meteorology from the University of Reading before training to become a teacher. She is passionate about teaching, having spent 8 years teaching GCSE and A Level Mathematics both in the UK and internationally. Amber loves creating bright and informative resources to help students reach their potential.

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