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2. TheDiscriminant TheNatureofRoots b24ac Fromthequadraticformulaisknownasthediscriminant.Itallowsustodetermineiftherootsarerealorimaginary.Iftherootsarerealitalsoallowsustodetermineifthereareoneortwo roots.2 3. b24ac>0 TherearetworootsIfb24acisaperfectsquaretherootsarerationalIfb24acisnotaperfectsquaretherootsare irrational 3 4. b24ac=0 ThenthereisonlyonerealrootThefunctiononlycrossesthexaxisatthevertexofthe parabola 4 5. b24ac