This key facts covers The Key Insight within Solving Quadratics for GCSE Mathematics. Revise Solving Quadratics in Algebra for GCSE Mathematics with 15 exam-style questions and 12 flashcards. This topic shows up very often in GCSE exams, so students should be able to explain it clearly, not just recognise the term. It is section 2 of 8 in this topic. Use this key facts to connect the idea to the wider topic before moving on to questions and flashcards.
The Key Insight
If A × B = 0, then either A = 0 or B = 0 (or both)
This is why factorising works! If we can write:
x² + 5x + 6 = 0 as (x + 2)(x + 3) = 0
Then either (x + 2) = 0 → x = -2
Or (x + 3) = 0 → x = -3
Practice questions for Solving Quadratics
The equation x² + 5x + 10 = 0 has:
A rectangle has length (x + 5) cm and width (x + 2) cm. The area of the rectangle is 40 cm². Form a quadratic equation and solve it to find the value of x.