Let \(a, b \) be real numbers, and let \(x_1\), \(x_2\) be the roots of the quadratic equation \(x^{2}+ax+b=0\). Prove that if \(x_1, x_2\) are real and nonzero, \(\frac 1{x_1}+\frac 1{x_2}<1\), and \(b>0\), then \(|a+2| >2\).

My real complaint though is that if a person is too lazy to write their question properly then they will be too lazy to put the effort needed into understanding any answer they are given.

I'm sorry you felt that way. I really do appreaciate all answers everyone teaches me. Many of you guys have helped me a lot, and yes, I will change the latex.