Practical context for a quadratic equation with negative discriminant.

Question

I'm looking for practical questions that lead to quadratic equations with negative discriminant. The pupils involved are 16 years old and technically educated.

Abstract mathematic questions are quite easy to create, e.g. "We're looking for two numbers, whose sum is 5 and product 7", but I'd like 'real world' examples.

I imagine that electrical calculations could probably be used, but I'm afraid I'm not technically educated myself (alas).

EDIT

What I'm really looking for is an example where the question and the solutions to the equation are somehow 'connected' to the real world.

Answer 1

The historical context was that such equations appeared in the solution of cubic equations that were known to have real solutions and this led to the invention of complex numbers.

Answer 2

They are too early in their mathematical careers to understand what a differential equation is, but you could explain that for instance, when there is a spring with a weight tied to the end, then there is a quadratic polynomial whose discriminant is negative/positive according as to whether the spring will oscillate or not when released.

Answer 3

You have 5 meters fence. Is it possible to build a rectangular pen with that fence with area 7 square meters?