Reason for no IRR for some projects

Why for some projects there will no Internal Rate of Return (IRR) ? I am not looking for numerical example. A simple logical explanation is enough.

Solving for IRR is essentially finding the roots of a polynomial; not all polynomials have real roots (e.g., x^2 + 1).

Thanks for your reply

My pleasure.

Why is it that in case of mutually exclusive projects, if discount rate is less than cross over rate, NPV method ranks projects differently from the IRR method and the same does not happen if discount rate is more than cross over rate ? I am not looking for calculations. Just a simple explanation is enough