AlgebraIntroduction

When Factorising Fails

Part of Quadratic Formula · GCSE GCSE Mathematics revision

This introduction covers When Factorising Fails within Quadratic Formula for GCSE Mathematics. Revise Quadratic Formula in Algebra for GCSE Mathematics with 11 exam-style questions and 5 flashcards. This topic appears regularly enough that it should still be part of a steady revision cycle. It is section 1 of 8 in this topic. Use this introduction to connect the idea to the wider topic before moving on to questions and flashcards.

Topic position

Section 1 of 8

Practice

11 questions

Recall

5 flashcards

When Factorising Fails

Not every quadratic can be factorised nicely. Try factorising x² + 3x - 7 = 0... you can't! The solutions aren't nice whole numbers. That's when the quadratic formula saves the day - it works for EVERY quadratic equation, giving you exact answers (often involving surds).

Visual: The Discriminant and Number of Solutions

Diagram showing the quadratic formula x = (-b ± √(b² - 4ac)) / 2a and three parabolas illustrating the discriminant: when b² - 4ac > 0 (two solutions, parabola crosses x-axis twice), when = 0 (one repeated root, parabola touches x-axis), and when < 0 (no real solutions, parabola doesn't touch x-axis).

Keep building this topic

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

THE Formula (Memorise This!)Method: Using the Quadratic Formula Worked Example 1: Clean Numbers

Practice Questions for Quadratic Formula

For the equation 3x² − 5x + 2 = 0, what are the values of a, b, and c in the quadratic formula?

A. a = 3, b = 5, c = 2
B. a = 3, b = −5, c = 2
C. a = −5, b = 3, c = 2
D. a = 3, b = −5, c = −2

1 markfoundation

Explain what the value of the discriminant (b² − 4ac) tells you about the solutions to a quadratic equation.

2 marksstandard

Quick Recall Flashcards

Quadratic Formula

x = (-b ± √(b²-4ac))/2a for ax² + bx + c = 0

The Quadratic Formula

x = (-b ± √(b² - 4ac)) / 2a

11 questions on Quadratic Formula — practise free

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Quadratic Formula

THE Formula (Memorise This!)