Question

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

Answer 1

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