How to solve a quadratic equation with a linear algorithm?

Question

Algorithms

And so, the essence of the question: recently there was a control in computer science, where my teacher said that it was impossible to solve a quadratic equation using a linear algorithm (that is, without cycles and conditions).
I thought, is it really all that hopeless? I've been trying to come up with something for about two days, but all attempts are in vain.. do you have any ideas?

Answer 1

So, is there a mathematical solution? That's right, without conditions in the text at all.
In my opinion - no. Because there may be quadratic equations that do not have roots, and this must still be checked.
But some specific special cases are quite possible.