GCSE · Quadratic equations

Solving quadratics by factorisingExam-style questions

Solve an equation with an $x^2$ in it by splitting it into two brackets. Eight short parts, from why zero makes it work to what the two answers look like on a graph, then the exam questions.

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16 questions · GCSE (Higher) level · mark scheme and worked solution on each · no sign-up to try

DifficultyAllLevel 1Level 2Level 3Level 4Level 5
  1. 1
    A rectangle has length (x+5)(x + 5) cm and width (x−2)(x - 2) cm.(x + 5) cm(x − 2) cmDiagram NOT accurately drawn

    The area of the rectangle is 60 cm².

    (a) Show that x2+3x−70=0x^2 + 3x - 70 = 0

    (b) Find the length and the width of the rectangle.
    Level 5 · 5 marksTry it
  2. 2
    Solve 12x−x=4\dfrac{12}{x} - x = 4, where x≠0x \neq 0.
    Level 5 · 4 marksTry it