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Cambridge 9709 · Pure Mathematics 1

Practise solving quadratic equations

Check your answers and use feedback to improve.

3 worked examples8 guided questionsFactors, roots and restrictions

Maths4U Original: notes, examples & two exam-style problems

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8 questions to work through

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How to enter answers

Enter both roots, separated by a comma, in either order. Use fractions such as -3/4 or decimals rounded to six decimal places.

Factorise and solve

1

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Solve the quadratic equation \(x^2 - 5x + 6 = 0\).

Enter both roots
Review the method

2

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Solve the quadratic equation \(x^2 - 7x + 10 = 0\).

Enter both roots
Review the method

3

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Solve the quadratic equation \(x^2 - 7x + 12 = 0\).

Enter both roots
Review the method

4

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Solve the quadratic equation \(x^2 - 8x - 20 = 0\).

Enter both roots
Review the method

5

Roots of a quadratic

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Find the roots of the equation \( x^2 + 5x + 6 = 0 \).
Enter both roots
Review the method

Rearrange and check restrictions

6

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Solve \( x^2 - 6x - 16 = 0 \)
Enter both roots
Review the method

7

Not checked
Solve: \(\quad x - \frac{6}{x-5} = 0\)
Enter both roots
Review the method

8

Not checked
Solve: \(\frac{5x+1}{4} - \frac{2x-1}{2} = x^2\)
Enter both roots
Review the method

Keep practising

Open all 9 questions in this topicTry 4 exam questionsCompleting the square