Quadratic Formula

MathematicsAQAEdexcelGCSEUnit: Algebra
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The basics

When Factorising Fails

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).
Exam tip

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Common Mistakes to Avoid

  • WRONG: Forgetting the negative in front of b → writing b instead of -b
  • WRONG: Writing -b² instead of (-b)² when b is negative (Use brackets!)
  • WRONG: Forgetting to divide the WHOLE top by 2a
  • RIGHT: Calculate b² - 4ac separately first, then substitute

Now try it yourself

Quiz · Question 1 of 11

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

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This topic in real past papers

Every real exam question we've found on quadratic formula, with a full worked answer.

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