[" If "f(x)=prod_(i=1)^(3)(x-a_(i))+sum_(i=1)^(3)a_(i)-3x" where "a_(i)

If f(x)=Pi_(i=1)^(3)(x-a_(i))+sum_(i=1)-3a_(i)-3x where a_(i)

If f(x)= prod_(i=1)^3 (x-a_i) +sum_(i=1)^3a_i-3x where a_i lt a_(i+1) forall i=1,2,. . . then f(x)=0 has

If f(x) =Pi_(i=1)^3(x-a_i) + sum_(i=1)_3 a_i - 3x where a_i < a_(i+1) for i = 1,2, then f(x) = 0 have

If f(x) =Pi_(i=1)^3(x-a_i) + sum_(i=1)_3 a_i - 3x where a_i < a_(i+1) for i = 1,2, then f(x) = 0 have

If f(x)=prod_(n=1)^(100)(x-n)^(n(101-n)), where prod_(i=1)^(k)a_(i) stands for product a_(1)dot a_(2).........a_(k), then (f(101))/(f'(101))=(a)5050( b) (1)/(5050) (c) 10010 (d) (1)/(10010)

a_(i)in R-{0},i=1,2,3,4 and x in R and (sum_(i=1)^(3)a_(i)^(2))x^(2)-2x(sum_(i=1)^(3)a_(i)a_(i+1))+sum_(i=2)^(4)a_(i)^(2)<=0,a_(1),a_(2)

If the arithmetic mean of a_(1),a_(2),a_(3),"........"a_(n) is a and b_(1),b_(2),b_(3),"........"b_(n) have the arithmetic mean b and a_(i)+b_(i)=1 for i=1,2,3,"……."n, prove that sum_(i=1)^(n)(a_(i)-a)^(2)+sum_(i=1)^(n)a_(i)b_(i)=nab .

If the arithmetic mean of a_(1),a_(2),a_(3),"........"a_(n) is a and b_(1),b_(2),b_(3),"........"b_(n) have the arithmetic mean b and a_(i)+b_(i)=1 for i=1,2,3,"……."n, prove that sum_(i=1)^(n)(a_(i)-a)^(2)+sum_(i=1)^(n)a_(i)b_(i)=nab .

If the arithmetic mean of a_(1),a_(2),a_(3),"........"a_(n) is a and b_(1),b_(2),b_(3),"........"b_(n) have the arithmetic mean b and a_(i)+b_(i)=1 for i=1,2,3,"……."n, prove that sum_(i=1)^(n)(a_(i)-a)^(2)+sum_(i=1)^(n)a_(i)b_(i)=nab .