This problem from a recent edition of Halliday & Resnick (& whoever)...
In the x-y plane there are equal charges +q placed on the y axis at (0,D) and (0,-D). Let E(x) be the field at a point (x,0) on the x axis. Let a = x/D be the x position scaled to the y distance D.
(a) Find the value of a where E(x) = E(aD) is a maximum.
Note: This is eminently fair, and the answer is a = 1/√2. It's a pretty good elementary problem. The questionable part comes next:
Find the values of a where E is one half the maximum value. (b) and (c) ask for these two values. The Wiley website asks for something like 2% accuracy, and accepted a numerical solution obtained with the use of technology.
Is it fair to have a problem that can't be solved analytically using methods that the student has studied? Unless I'm missing something, this involves solving an unfactorable cubic, and nobody tortures lower-division math students with the cubic formula. They get an introduction to numerical integration in Calc I, typically, but most won't have taken a numerical analysis class.
So, is there a way to get a 2% answer to this without technology using methods that a student would be expected to have covered?
If not, is it sensible to even ask such a question? By today's standards, of course. When I took the course, it would have been unthinkable.