When Factorising Fails

Part of Quadratic Formula · Section 1 of 8

IntroductionUnit: AlgebraGCSE

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.

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).

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

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