Question
Wed August 31, 2011 By:

If the zeros of the polynomial f(x)=ax3+3bx2+3cx+d are in A.P.,prove that 2b3-3abc+a2d=0

Expert Reply
Wed August 31, 2011
Let A-D,A,A+D be the roots of the cubic polynomial.
Then,Sum of roots=(A-D)+A+(A+D)=3A=-3b/a
Thus,A=-b/a,Which is a root of the polynomial .
Hence,satisfies it,
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