A second-order polynomial sequence is of Fibonacci-type (Lucas-type) if its Binet formula has a structure similar to that for Fibonacci (Lucas) numbers. Known examples of these types of sequences are Fibonacci polynomials, Pell polynomials, Fermat polynomials, Chebyshev polynomials, Morgan-Voyce polynomials, Lucas polynomials, Pell-Lucas polynomials, Fermat-Lucas polynomials, and Chebyshev polynomials.

The resultant of two polynomials is the determinant of the Sylvester matrix and the discriminant of a polynomial p is the resultant of p and its derivative. We study the resultant, the discriminant, and the derivatives of Fibonacci-type polynomials and Lucas-type polynomials as well the resultant of combinations of these two types of polynomials. As a corollary, we give explicit formulas for the resultant, the discriminant, and the derivative for the polynomials mentioned above.