A positive sum rules out three negative summands

the roots are $\frac{a+b+c\pm \sqrt{\Delta}}{2}$ have the real part $a+b+c$ which is equal to $\alpha$ and greatest than $0$ . So $a,b,c$ cannot be three negative numbers.

Source: InternLM Lean-Workbook, record lean_workbook_48897 (Apache-2.0). The complete source proposition and explicit variable declarations are preserved.