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Let f(x)=x^(3)-9x^(2)+24x+c=0 have three...

Let `f(x)=x^(3)-9x^(2)+24x+c=0` have three real and distinct roots `alpha, beta` and `lambda`.
(i) Find the possible values of c.
(ii) If `[alpha]+[beta]+[lambda]=8`, then find the values of c, where `[*]` represents the greatest integer function.
(ii) If `[alpha]+[beta]+[lambda]=7`, then find the values of c, where `[*]` represents the greatest integer function.s

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To solve the problem step by step, we will break it down into parts as per the question. ### Given: The polynomial function is: \[ f(x) = x^3 - 9x^2 + 24x + c = 0 \] ### Part (i): Find the possible values of \( c \) ...
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