# Do SawaaL

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.

106
Asish Mahapatra ·

1. pls recheck the question .. the last two terms

13
Avik ·

1) POlynomial toh yahi given hai...i didn't writ p(x) =0 bas, rest is same.

2) ans is 2007.

106
Asish Mahapatra ·

arey 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

13
Avik ·

chcked bhai, tabhi toh confusion hai ! Ans is given 2 rational roots!

13
Avik ·

Sol.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 Îµ R.

1
Che ·

1) rational root theorem can be applied here ?

13
Avik ·

No idea Che [4], u try n see.

39
Pritish Chakraborty ·

Rational 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

1
Che ·

ok 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

13
Avik ·

Tht sol.n given in the book (#6) is wrong naa ?

Anonymous ·

The last 2 terms are 3x+2 now tell the solution plzz