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Solving Hidden Quadratics using Substitutions (AQA AS Maths): Revision Note

Exam code: 7356

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AQA Maths: PureCambridge (CIE) Maths: Pure 1OCR Maths A: PureEdexcel Maths: Pure

Solving hidden quadratics using substitutions

What are hidden quadratic equations?

  • Hidden quadratic equations are quadratics written in terms of a function f left parenthesis x right parenthesis

  • A normal quadratic appears in the form a x squared plus b x plus c equals 0

  • Whereas a hidden quadratic appears in the form a open square brackets f left parenthesis x right parenthesis close square brackets squared plus b open square brackets f left parenthesis x right parenthesis close square brackets plus c equals 0

  • This might look complicated but it simply means x has been replaced by f left parenthesis x right parenthesis

  • e.g. sin squared space x plus 2 sin space x minus 3 equals 0 is just the hidden quadratic of x squared plus 2 x minus 3 equals 0 where f left parenthesis x right parenthesis space equals space sin space x

How do I solve hidden quadratic equations?

  • First rearrange the function into the form a open square brackets f left parenthesis x right parenthesis close square brackets squared plus b open square brackets f left parenthesis x right parenthesis close square brackets plus c equals 0

  • Replacing the function and solving the 'normal' quadratic first

  • Then substitute the function back into the solutions to solve the original quadratic

    Further Solving of Quadratic Equations Notes Diagram 2, A Level & AS Level Pure Maths Revision Notes

Worked Example

Further Solving of Quadratic Equations Example, A Level & AS Level Pure Maths Revision Notes

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    Paul has taught mathematics for 20 years and has been an examiner for Edexcel for over a decade. GCSE, A level, pure, mechanics, statistics, discrete – if it’s in a Maths exam, Paul will know about it. Paul is a passionate fan of clear and colourful notes with fascinating diagrams.