let x1>x2>x3>x4> ...................>x6>0,A = x1 + ......... x6 .B = x1x3

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1)let x1>x2>x3>x4> ...................>x6>0,A = x1 + ......... x6 .B = x1x3 + x1x5 + x3x5+ x2x4 + x2x6 +x4x6.C = x1x3x5 + x2x4x6 .then the eqnn 2x^3 - Ax^2 +Bx - C = o has a-excatly 1 real rootb-3 +ve rootsc- 3 -ve rootsd-none of these

2)let A,B,C be the angles of triangle and tanA,tanB,tanC be the 3 roots of x^{4 }- ax^{3 }+bx^{2} - cx + d = o , then the fourth root is also root of -----------------

3)let p(x) be a polynomial with integral co-efficients such that p(0) and p(1) r both odd integers then the no of integral rootes of p(x) =0 is

Joined:24 Dec 2007Posts:11111)Since A, B and C are all positive (coz of given conditions)...we have a cubic eqn of type Dx^3 - Ax^2 +Bx - C, where A,B,C,D are all positive.... so U can use Descartes' rule of signs