Let $a,b$ be two distinct roots of $x^4+x^3-1=0$ and $p(x)=x^6+x^4+x^3-x^2-1$

Question

$\begin{array}{1 1}(A)\;\text{a+b is a root of p(x)=0}\\(B)\;\text{ab is a root of p(x)=0}\\(C)\;\text{Both a+b and ab are root of p(x)=0}\\(D)\;\text{Neither a+b nor ab is a root of p(x)=0}\end{array}$