Here’s a further undergraduate contribution to the theory of quadratic equations, taken from my most recent plague of marking. The context is a final-year exam; notation has been changed to protect the guilty, but not enough to affect the difficulty of the task.
The task in question: given the equation
where and are constants, solve for , then find .
Out of twenty students, three arrived independently at the solution
and differentiated happily on the basis that on the RHS was a constant. One arrived at the solution
and likewise differentiated assuming that on the RHS was a constant. And one student wrote:
As I can’t reduce only one side to “”, I am assuming .
And one examiner wept silently into his coffee.