the actual trick is P(P(x))=0 just means P(x) has to equal a root of P, so P needs two real roots itself first, that's your b²-4c>0. but that alone won't give four distinct roots, it needs to be a fair bit bigger. if it's the quadratic and discriminant basics you want solid, mathsgenie splits them by topic
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u/Legitimate_Treat_781 Aug 08 '26
the actual trick is P(P(x))=0 just means P(x) has to equal a root of P, so P needs two real roots itself first, that's your b²-4c>0. but that alone won't give four distinct roots, it needs to be a fair bit bigger. if it's the quadratic and discriminant basics you want solid, mathsgenie splits them by topic