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Worked Example

Part of Quadratic Inequalities — GCSE Mathematics

This study notes covers Worked Example within Quadratic Inequalities for GCSE Mathematics. Revise Quadratic Inequalities in Algebra for GCSE Mathematics with 10 exam-style questions and 2 flashcards. This topic appears less often, but it can still be a useful differentiator on mixed-topic papers. It is section 4 of 4 in this topic. Use this study notes to connect the idea to the wider topic before moving on to questions and flashcards.

Topic position

Section 4 of 4

Practice

10 questions

Recall

2 flashcards

Worked Example

Solve: x² − 5x + 6 < 0

Step 1 Find roots

x² − 5x + 6 = 0

(x − 2)(x − 3) = 0

x = 2 or x = 3

Step 2 Sketch and identify

Positive x² = U-shaped parabola

Crosses x-axis at x = 2 and x = 3

Below x-axis (< 0) BETWEEN the roots

Step 3 Write solution

2 < x < 3

Keep building this topic

Read this section alongside the surrounding pages in Quadratic Inequalities. That gives you the full topic sequence instead of a single isolated revision point.

Key PatternsAbove or Below the Curve?Method

Practice Questions for Quadratic Inequalities

For a positive (U-shaped) parabola with roots at x = 2 and x = 5, the expression is negative (below the x-axis) for which values of x?

  • A. x < 2 or x > 5
  • B. 2 < x < 5
  • C. x < 2 and x > 5
  • D. All values of x
1 markfoundation

Explain what the solution set of x² + 2x + 5 > 0 is, justifying your answer using the discriminant.

2 marksstandard

Quick Recall Flashcards

Quadratic Inequality Pattern
For U-shape: > 0 = outside roots (x < a or x > b), < 0 = between roots (a < x < b)
Quadratic Inequalities
Sketch graph, identify where curve is above/below x-axis

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Quadratic Inequalities