AlgebraIntroduction

Why Two Solutions?

Part of Solving QuadraticsGCSE Mathematics

This introduction covers Why Two Solutions? 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 1 of 7 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 7

Practice

15 questions

Recall

12 flashcards

Why Two Solutions?

Quadratic equations have an x² term, which means the graph is a PARABOLA (U-shape). A parabola can cross the x-axis at TWO points, ONE point, or ZERO points. Each crossing point gives you a solution. When we solve by factorising, we're finding where the parabola crosses the x-axis!

Keep building this topic

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

Practice Questions for Solving Quadratics

The equation x² + 5x + 10 = 0 has:

  • A. Two different real solutions
  • B. One repeated solution
  • C. No real solutions
  • D. Infinitely many solutions
1 markfoundation

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.

3 marksstandard

Quick Recall Flashcards

Solving Quadratics
Set equal to 0, factorise, each bracket = 0
How to factorise x² + bx + c
Find two numbers that: - Multiply to give c - Add to give b Then write as (x + p)(x + q)

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