If  x6 - 12x5 + ax4 + bx3 + cx2 + dx + 64 = 0  has positive roots then find a,b,c,d. 

Assume any 6 roots (positive) , AM of roots taken one at a time > GM of roots.
Here you will find that AM=GM. This implies that all the roots must be equal. Now you know the roots, just calculate it.
  • -6
a=12,b=-12,c=12,d=-76
  • -9
Above polynomial is (x-2)^6,
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  • 1
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