Question

why b2-4ac called discriminant?

Answer 1

The quantity b2 − 4ac that appears under the square root is called the discriminant and is denoted ∆. If ∆ = b2 − 4ac > 0 then the equation has two distinct real solutions. If ∆ = b2 − 4ac = 0 then the equation has exactly one real solution. If ∆ = b2 − 4ac < 0 then the equation has no real solutions.
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Answer 2

the word discriminant means something which categorise another thing and also b^2-4ac was defined by shridharacharya to classify roots of a quadratic equation