If `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 leq 0,a_1,a_2,a_3,a_4` are in

If a_iepsilon R-[0},i=1,2,3,4 and xepsilon R and (sum_(i=1)^ a_i^2) x^2-2x(sum_(i=)^3 a_ia_(i+1)+)+sum_(i=2)^4 a_i^2ge0 then a_1,a_2,a_3,a_4 are in (A) A.P. (B) G.P. (C) H.P. (D) none of these

a_1,a_2,a_3 ,…., a_n from an A.P. Then the sum sum_(i=1)^10 (a_i a_(i+1)a_(i+2))/(a_i + a_(i+2)) where a_1=1 and a_2=2 is :

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 b_i=1-a_i ,n a=sum_(i=1)^n a_i ,n b=sum_(i=1)^n b_i ,t h e nsum_(i=1)^n a_i ,b_i+sum_(i=1)^n(a_i-a)^2= a b b. n a b c. (n+1)a b d. n a b

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

Let A be the set of vectors veca=(a_1,a_2,a_3) satisfying (sum_(i=1)^3a_i/2^i)^2=sum_(i=1)^3a_i^2/2^i Then