6. If the roots of the equation $x^{2}+3 x-1=0$ are also the roots of the equation $x^{4}+a x^{2}+b x+c=0$, find the value of $a+b+4 c$.
(A) -13
(B) -7
(C) 5
(D) 7
(E) 11
6. Answer:
(B)
We have the factorization
$$
\left(x^{2}+3 x-1\right)\left(x^{2}+m x-c\right)=x^{4}+a x^{2}+b x+c .
$$

Comparing coefficients give $3+m=0,-1-c+3 m=a$ and $-3 c-m=b$. We can solve these equations to obtain $a+b+4 c=-7$.