Answer
$(-\frac{1}{3}, -\frac{5}{9})$ and $(-5,1)$
Work Step by Step
Step 1. $x^2+5x+1=-2x^2-11x-4 \longrightarrow 3x^2+16x+5=0 \longrightarrow (3x+1)(x+5)=0 \longrightarrow x=-\frac{1}{3}, -5$
Step 2. For $x=-\frac{1}{3}$, we have $f(-\frac{1}{3})=(-\frac{1}{3})^2+5(-\frac{1}{3})+1=-\frac{5}{9}$
Step 3. For $x=-5$, we have $f(-5)=(-5)^2+5(-5)+1=1$
Step 4. The intersect points are $(-\frac{1}{3}, -\frac{5}{9})$ and $(-5,1)$
