A polynomial of degree 4 is necessarily a product of two polynomials of degree 2.
This has to do with the d'Alembert-Gauss theorem, which states that any polynomial can be developped into a product of polynomial of degree 1 containing complex numbers.
However, I don't know (or don't remember I've learnt it..) why a polynomial can always be a product of polynomials of degree 1 or 2...
Getting back to the problem :
Develop in order to find a, b, c and d...
Edit : it seems that the first attempts are vain for solving..
might be of indirect interest to you.