8. For positive integer $a$ and integers $b$, $c$, the quadratic equation $a x^{2}+b x+c=0$ has two roots $\alpha$, $\beta$. And it satisfies $0<\alpha<\beta<$ 1. Find the minimum value of $a$.
8. Let $f(x)=a x^{2}+b x+c$, then $f(0)=c>0, f(1)=a+b+c>0, \Delta=b^{2}-4 a c>0.0c>0, 0-(a+c)+1 .(\sqrt{a}-\sqrt{c})^{2}>1, \sqrt{a}>\sqrt{c}+1 \geqslant 2$, so $a \geqslant 5$. And when the equality holds, $c=1, b=-5$. That is, $a_{\text {min }}=5$.