Polynomials
Given the equation:

Where all the coefficients are real numbers, and it has 3 real roots of the form:

It has two imaginary roots of the form: di and -di. Recall both roots must be conjugated.
a) Knowing the sum of the roots must be equal to the inverse negative of the coefficient of the fourth-degree term:

b) It's additionally given the values of a, b, and c are consecutive terms of a geometric sequence. Assume that sequence has first term a1 and common ratio r, thus:

Using the relationship found in a):

As said above, the real roots are:

Since b = a1*r, then b = 2, thus:

One of the real roots has been found to be 1. We still don't know the others.
c) We know the product of the roots of a polynomial equals the inverse negative of the independent term, thus:

Since q = 8 d^2:

From the relationships obtained in a) and b):

Substituting:

Simplifying:

We'll take the positive root only:

Thus:

The other roots are:

Real roots: -2, 1, 4