Really struggling with this question.

Let R=C[X] (complex)

S={f(X) = (sum from i=0 to n) a_{i}X^{i}in C[X] : a_{2}= 0} and

T={f(X) = (sum from i=0 to n) a_{i}X^{i}in C[X] : a_{1}= 0}

S and T are the sets of polynomials with coefficients in C and with zero quadratic, respectively linear, term.

Prove that S is not a subring of R

Prove that T is a subring of R, but not an ideal or R.

Any help much appreciated!!