[ Research on quadratic trinomials ] [ Examples and counterexamples. Constructions ]

It is known that $b-c>a$ and $a \neq 0$. Is it necessarily true that the equation $a x^{2}+b x+c=0$ has two roots?
Counterexample: $a=c=-1, b=1.1-(-1)>1$, but the equation $-x^{2}+x-1$ has no roots.

## Answer

Not necessarily.