Let $x^2-ax+b$ be a polynomial with real coefficients having two nonzero roots. Given that $|b+1|<a$, and one of the roots have modulus $<1$, show that the other root has modulus $>1$.
We can assume the two roots are $x_1,x_2$. We have the information that $|x_1x_2+1|<x_1+x_2$, and say $|x_1|<1$. How to conclude that $|x_2|>1$?
[Source: Russian competition problem]