Determine by the order of transfer function what kind of filter
You could guess the form of the frequency response of the filter if you knew the poles and the zeroes of any TF. Then drawing the poles and the zeroes in the complex plane you could tell something about that.

In your case there is no zero (numerator is constant). So you have a denominator which is a 3rd order polynomial. To find the poles you must find the roots of that polynomial, which are a function of the coefficients a,b,c.

For algebraic equations up to the 4th order there are general formulas to find those roots. See here for 3rd order and here for 4th order.

Anyway, a 3rd order equation with real coefficients (assuming a,b,c are real) will have at least a real root and either another two real roots or a couple of complex conjugate roots.