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Year 10 · Patterns & Algebra

Solve quadratic equations

A quadratic equation has an x² term and usually two solutions. Factorising finds them.

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How to do it

  1. Make one side zero.
  2. Factorise into two brackets.
  3. Set each bracket to zero and solve.

Worked example

Solve x² − 4x − 12 = 0. What is the smaller solution?
Factorise: two numbers that multiply to -12 and add to -4 are -6 and 2. So (x − 6)(x + 2) = 0, giving x = 6 or x = -2.
Answer: -2

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Both solutions count; give the one the question asks for.

Practise Solve quadratic equations properly

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