In C++, ask the user for the constant coefficients of a quadratic equation ax²+bx+c =0 (a, b & c) and have the function return the two roots by solving using the quadratic formula. You should display a message if the user enters coefficients that result in roots that are imaginary along with the real and imaginary roots. Create a program so that it will run so long as the user would like to test values.

Ensure to utilize pass by reference as well as a flowchart for starters.