The discriminant is b squared minus 4ac. Positive means two real roots, zero means one, negative means none. You do not have to finish the quadratic formula to count the solutions. The formula itself is in the quadratic formula.
Count, then stop
For x² − 5x + 6, b² − 4ac = 25 − 24 = 1, two roots. Graphing those roots is in finding x-intercepts.
Quadratics in Desmos are in quadratics in Desmos. The short list is in ACT Math formulas.
The bottom line
b² − 4ac. Sign tells you how many real solutions.
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