AlgebraTopic Summary
Knowledge Organiser: The Quadratic Formula
This topic summary covers Knowledge Organiser: The Quadratic Formula 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 8 of 8 in this topic. Use this topic summary to connect the idea to the wider topic before moving on to questions and flashcards.
Topic position
Section 8 of 8
Practice
11 questions
Recall
5 flashcards
Knowledge Organiser: The Quadratic Formula
Key Terms
- Quadratic formula: A formula that solves any quadratic ax² + bx + c = 0
- Discriminant: b² − 4ac — determines how many solutions exist
- Coefficients a, b, c: From ax² + bx + c = 0 (note: c can be negative)
- Exact answer: An answer in surd form (not a rounded decimal)
- Surd: An irrational square root left in the form √k
Must-Know Facts
- If b² − 4ac > 0: two distinct solutions
- If b² − 4ac = 0: one repeated solution (x = −b ÷ 2a)
- If b² − 4ac < 0: no real solutions
- Always rearrange to ax² + bx + c = 0 BEFORE identifying a, b, c
- The ± gives two solutions: one with + and one with −
- Calculate b² − 4ac first, then substitute carefully
- This formula must be memorised — it is NOT given on the formula sheet
Key Formulas
- x = (−b ± √(b² − 4ac)) ÷ 2a
- Discriminant: b² − 4ac
- b² − 4ac > 0 → 2 roots; = 0 → 1 root; < 0 → no real roots
Common Mistakes
- Forgetting the ± : The formula gives TWO solutions — always write both x = (−b + √…)/2a AND x = (−b − √…)/2a
- Dividing only part of the numerator: The entire expression −b ± √(b²−4ac) is divided by 2a, not just the √ part
- Sign of b: If b is negative (e.g. b = −5), then −b = +5 — take care with negatives
- Not rearranging first: Must have ax² + bx + c = 0 before identifying a, b, c
- Rounding too early: Keep √(b²−4ac) exact until the final step to maintain accuracy