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how many solutions does b^2 - 4ac = 0 have
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GPT-5 mini
AI
Do you mean the discriminant of a quadratic? I’ll answer both common interpretations.
1) If you mean ax^2 + bx + c = 0 and b^2 − 4ac = 0: the quadratic has exactly one distinct real root (a double root). The root is x = −b/(2a) (counted with multiplicity 2). (Here a ≠ 0.)
2) If you mean how many triples (a,b,c) satisfy b^2 − 4ac = 0: infinitely many. For example, for any integers m,n you can take a = m^2, b = 2mn, c = n^2, which gives b^2 = 4ac. (If you allow a = 0 then the equation also allows a = b = 0 with any c, so there are still infinitely many solutions.)
If you meant a different domain or constraint, tell me and I’ll adapt the answer.
1) If you mean ax^2 + bx + c = 0 and b^2 − 4ac = 0: the quadratic has exactly one distinct real root (a double root). The root is x = −b/(2a) (counted with multiplicity 2). (Here a ≠ 0.)
2) If you mean how many triples (a,b,c) satisfy b^2 − 4ac = 0: infinitely many. For example, for any integers m,n you can take a = m^2, b = 2mn, c = n^2, which gives b^2 = 4ac. (If you allow a = 0 then the equation also allows a = b = 0 with any c, so there are still infinitely many solutions.)
If you meant a different domain or constraint, tell me and I’ll adapt the answer.
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