Let a1,a2,a3,a4 and a5 are the roots of x5−ax4+bx3−cx2+dx−1=0 If AM and GM of a1,a2,a3,a4 and a5 are equal, then a1=a2=a3=a4=a5=1 Sum of roots =5C1=5 ∵a=5 Sum of roots taken 2 at a time =5C2=10 ∴b=10 Sum of roots taken 3 at a time =5C3=10 ∴c=10 Sum of roots taken 4 at a time =5C4=5 ∴d=5 Hence, a+b+c+d=5+10+10+5=30