You are mystifying ...

I pointed out your error. If you do not agree, please justify.

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A quadritic polynomial has two roots in complex domain. [elementary knowlege]

we know that f(x) is quadritic polynomial [given condtions]

so f(x) has two roots, which are b and 2 [2 is known root, given condtions]

we know also f(5) is a root of f(x) [f(f(5)) = 0, given condtions]

f(5) = 3a(5-b) [simple calcul according to your expression of f(x)=a(x-2)(x-b)]

so f(5) = 3a(5-b) = b, or f(5) = 3a(5-b) = 2 [elementary knowlege]

combined with b=3+p,a=2/(6-3p) [your conclusion]

I get p=-1,a=2/9，b=2 [I'm not strong in calcul, please point out my error, thanks!]

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my teacher told me: a real number is also a complex number, do you agree with him? or have you a mystified defintion of complex number?

[ZT] 我不明白您不肯承认我的解法处于什么心理，不过我觉得挺没意思的。---说了就走