GCSE · Quadratic equations

The quadratic formulaExam-style questions

Where the formula comes from, how to substitute negative coefficients without sign disasters, and what the value under the square root says about how many solutions exist.

Start practising Read the lesson

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

DifficultyAllLevel 3Level 4Level 5
  1. 1
    Solve 3x2−8x+2=03x^2 - 8x + 2 = 0

    Give your answers correct to 3 significant figures.
    Level 4 · 3 marksTry it
  2. 2
    Solve 2x2+5x−4=02x^2 + 5x - 4 = 0

    Give your answers in surd form.
    Level 4 · 3 marksTry it
  3. 3
    Amir tries to solve x2+3x+5=0x^2 + 3x + 5 = 0 using the quadratic formula, but his calculator shows an error.

    Explain why the equation has no real solutions.
    Level 4 · 2 marksTry it
  4. 4
    Solve 2x2+3x−7=02x^2 + 3x - 7 = 0

    Give your answers correct to 3 significant figures.
    Level 4 · 3 marksTry it
  5. 5
    Solve 3x2−6x+1=03x^2 - 6x + 1 = 0

    Give your answers in the form a±bc\dfrac{a \pm \sqrt{b}}{c}, simplified as far as possible.
    Level 4 · 3 marksTry it