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When a quadratic equation does not have real roots

For any equation as ax2 + bx + c = 0 we have b2 - 4ac or DELTA smaller than zero thus having no real roots if:

  1. a, c > |b|
  2. a = b = c
  3. 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.