Given x2 < 1/100
so, x < 1/10 or x > - 1/10 first statement
also, as per question x < 0 second statement
so, intersection of both statement will be
- 1/10 < x < 0
Solution: ((x^999 x^998 ... x 1)^2-x^999)/(x^998 x^997 ... x 1)
=> ((x^999 x^998 ... x 1)^2-x^999)/(x^999 x^998 ... x 1)-x^999 or,
=>(x^998 ... x 2)^2-1/(x^998 ... x 2)-1 [taking x^999 as common and cancelling it]
we can now use the identity a^2-b^2=(a b)*(a-b)
using this we can see that p(x) is clearly divisible by q(x)
i.e. p(x)/q(x)= (x^999 x^998 ... x 1) x^999
so the remainder will be 0
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Choose the correct option.
In this question, A^B means A raised to power B. If x^2*y*z < 0, then which one of the following statements must also be true?
I. yz < 0
II. z < 0
III. x < 0
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