Evaluate the number of possible combinations of roots for a given polynomial equation. For example for quadratic, you can have:
- 2 imaginary roots (conjugate)
- two real distinct roots
- or 1 repeated root.
In this case, we have only 3 possible combinations For cubic you can have:
- 3 distinct real roots
- 3 repeated real roots
- 2 repeated and 1 distinct real roots
- 2 distinct imaginary (conjugate) and 1 real
- 1 repeated imaginary (conjugate) and 1 real and in this case we have 5 possible combinations:
can you find a formula that gives the total number combinations, for example, 3 for quadratics and 5 for cubic equations, for any given polynomial of degree n?