Find the condition that the zeros of the polynomial f (x) = x^3+3px^2+3px+r may be in A. P.

Step-by-step explanation:

note:

(a + b) ^3 = a^3 + b^3 + 3 a²b + 3b²a + b^3 ... (*)

the condition is : r = 1 and p=1

put : x = a and b = 1 in (*) you have:

(x + 1) ^3 = x^3 + 3x² + 3x + 1

the zeros is : x = - 1

bcause : x^3 + 3x² + 3x + 1 = 0 ... (x + 1) ^3 = 0 so : x = - 1