Having had several student queries on solving ‘hidden’ quadratic equations, I thought I would note some great resources available.
Firstly two videos on TL Maths, 3.15 and 3.16
From Dr Austin Maths try this practice exercise of 7 questions.
The resources on Dr Frost Maths are so good; I love the new slideshow format with the slide types, each created for specific pedagogical purposes.
Scroll down to Factorising and Solving Hidden Quadratics.
From Exam Solutions, a tutorial, Solving quadratic equations in some function of x is available.
Try this Hidden Quadratics activity from Swinton Maths:
A fill in the blank activity for hidden quadratics. All the quadratics are monic and factorisable, and the index equations have integer solutions (so no logarithms needed).
And finally, we could use a favourite Underground Maths task to spot the hidden quadratics!
To log or not to log – Underground Maths
A favourite Underground Maths resource I have used many times – To log or not to log? This has worked really well every time I have used it. The activity requires students to think about the methods which could be used to solve the various equations. In addition to working on indices and logarithms, I have always found that this task has exposed some misconceptions, with students trying to invent some new and invalid laws of logarithms!
This problem is classified as a Problem Requiring Decisions.
For more favourite Underground Maths tasks, see the Underground Maths series of pages.
We could, of course, illustrate these equations graphically; I looked at the solutions of the equation 4x4 −13x2 + 9 = 0 with a student on Desmos.
