### When a quadratic equation does not have real roots

For any equation as ax^{2} + bx + c = 0 we have b^{2} - 4ac
or DELTA smaller than zero thus having no real roots if:

- a, c > |b|
- a = b = c
- a = b and c > b for any positive b. You can swap a and c.

I have proved these but since it's trivial, I did not write them here.