Let A be number of integers for which both roots of the quadratic equation `x^2 + 2(p-3)x + 9 = 0` lie in` (-6,1).` If `2,g_1,g_2,g_3.........g_20` A are in G.P. then the value of `(g_4 xx g_17)/2` is

Let A be number of integers for which both roots of the quadratic equation x^(2)+2(p-3)x+9=0 lie in (-6,1) .If 2,g_(1),g_(2),g_(2),g_(3),......g_(20) A are in G.P.then the value of (g_(4)xx g_(17))/(2) is

suppose x1,x2 are the roots of the equation ax^2+bx+c=0 and x3 and x4 are the roots of the equation px^2+qx+r=0 If a, b, c are in G.P. as well as x_1, x_2, x_3, x_4 are in G.P., then p, q, r are in (i) A.P (ii)G.P (iii)H.P (iv)A.G.P

if g(x^(3)+1)=x^(6)+x^(3)+2 then the value of g(x^(2)-1) is

If a is A.M. of b and c and c, G_(1) , G_(2) ,b are in G.P., then find the value of G_(1)^(3)+G_(2)^(3)-2abc

Let a,b,c be the roots of the equation x^(4)+x^(3)+x^(2)+x-1=0. Let f(x)=x^(6)-6x^(2)+6x+7 and g(x)=px^(2)+qx+r , (p,q,r in R,p!=0). If f(a)=g(a); f(b)=g(b) and f(c)=g(c); then the value of (2)/(g(1)) is

If the first term of geometric progression g_(1),g_(2),g_(3),... is unity,then the minimum value of 4g_(2)+5g_(3) is equal to

Lef a, b be two distinct positive numbers and A and G their arithmetic and geometric means respectively. If a, G_(1),G_(2) , b are in G.P. and a, H_(1),H_(2) , b are in H.P., prove that (G_(1)G_(2))/(H_(1)H_(2))lt (A^(2))/(G^(2)) .

If a,A_(1),A_(2),b are in A.P., a,G_(1),G_(2),b are in G.P. and a, H_(1),H_(2),b are in H.P., then the value of G_(1)G_(2)(H_(1)+H_(2))-H_(1)H_(2)(A_(1)+A_(2)) is