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When a quadratic equation does not have real roots

For an equation like ax2 + bx + c = 0 we have b2 - 4ac or DELTA is smaller than zero thus having no real root if:
1- a,c > |b|
2- a=b=c
3- a=b and c>b for positive b. You can swap a and c
I've proved it but since it's trivial, I didn't put it here.