106arey the last two terms dont fit into the pattern
xeven has coeff 2 in the fisrt two terms while it has become odd in the last term
isiliye keh rahaa hoon check it ...
2. thinking
1) Find the no. of rational roots of-
P(x) = 2x98 + 3x97 + 2x96 + 3x95 +....+2x+3 =0
(Hence, find the roots too.)
2) Least degree of a polynomial with integral coeff. of which a= 31/2007 is a zero is-
a)223, b)669, c)2007, d)none of these.
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11 Answers
131) POlynomial toh yahi given hai...i didn't writ p(x) =0 bas, rest is same.
2) ans is 2007.
10613Sol.n given fr 1)-
P(x) = (2x+3)(x^{97} +x^{96}+...+1)\\ \\ =(2x+3)(x+1)(x^{96}+x^{94}+...+x^2+1)\\
Also, x^{96}+x^{94}+...+x^2+1 >1 for all x ε R.
39Rational root theorem se, list of rational solns of p(x) can be obtained by
x = \pm \frac {1, 3} {1, 2}
So x = 1, -1, \frac {1}{2}, -\frac{1}{2}, 3, -3, \frac {3}{2}, -\frac{3}{2}
This is the list of possible rational roots of p(x). Ab Horner scheme istamaal karke kaun nikaalega actual rational roots? :D
1ok after getting that list
1 ,1/2, 3, 3/2 cant be the roots....
so ur list gets reduced to 4
u hav to chose in between -1, -1/2, -3, -3/2