If $a,b\in R$ and $a \neq 0$ and quadratic $ax^2-bx+c=0$

Question

If $a,b\in R$ and $a \neq 0$ and quadratic $ax^2-bx+c=0$ has imaginary roots then $a+b+1$
why a+b+1 should be positive?

Answer 1

The roots of $ax^2-bx+c$ are given by $$ \frac{b\pm\sqrt{b^2-4ac}}{2}, $$ which are both complex if and only if $b^2-4ac<0$.