If teh zeros of the polynomial f(x)=ax3+3bx2+3cx+d are in A.P., prove that 2b3−3abc+a2d=0
Let p-r, p, p+r be the zeroes of equation,
Sum of roots = p - r + p + p + r = 3p =
p =
Now, p is a root of eqn. So put it in the equation:
Hence proved