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