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CIE AS Maths: Pure 1

Revision Notes

Home / AS / Maths: Pure 1 / CIE / Revision Notes / 1. Algebra & Functions / 1.1 Quadratics / 1.1.6 Further Solving Quadratic Equations (Hidden Quadratics)

1.1.6 Further Solving Quadratic Equations (Hidden Quadratics)

Name: Further Solving Quadratic Equations (Hidden Quadratics) (1.1.6) | CIE AS Maths: Pure 1 Revision Notes 2020 Membership
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What are hidden quadratic equations?

Hidden quadratic equations are quadratics written in terms of a function $f (x)$
A normal quadratic appears in the form $a x^{2} + b x + c = 0$
Whereas a hidden quadratic appears in the form $a {[f (x)]}^{2} + b [f (x)] + c = 0$
This might look complicated but it simply means $x$ has been replaced by $f (x)$
e.g. $\sin^{2} x + 2 \sin x - 3 = 0$ is just the hidden quadratic of $x + 2 x - 3 = 0$ where $f (x) = \sin x$

How to solve hidden quadratic equations

First rearrange the function into the form $a {[f (x)]}^{2} + b [f (x)] + c = 0$
Replacing the function and solving the 'normal' quadratic first
Then substitute the function back into the solutions to solve the original quadratic

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 – one of the many reasons he is excited to be a member of the SME team.

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CIE AS Maths: Pure 1

Revision Notes

1.1.6 Further Solving Quadratic Equations (Hidden Quadratics)

What are hidden quadratic equations?

How to solve hidden quadratic equations

Author: Paul

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