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.

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

DifficultyAll Level 3 Level 4 Level 5

1
Show that the equation $\dfrac{5}{x} + x = 7$ can be written as $x^2 - 7x + 5 = 0$ , and hence solve it.

Give your answers correct to 2 decimal places.
Level 5 · 4 marksTry it
2
(a) Show that the equation $x(x + 3) = 2x + 9$ can be written as $x^2 + x - 9 = 0$

(b) Hence solve $x(x + 3) = 2x + 9$ , giving your answers correct to 2 decimal places.
Level 5 · 5 marksTry it
3
The equation $kx^2 + 6x + 3 = 0$ , where $k$ is a positive constant, has exactly one solution (a repeated root).

Work out the value of $k$ .
Level 5 · 3 marksTry it