(1) if p(x) = 1+x+x²+x³...............x^m

and p(xⁿ) is divisable by  p(x) then find he relation between m and n.

(2) if a,b,c are positive integers

and the equaion ax²+bx+c has one root in (-1,0) and other root in (0,1).

if the least value of a+c=b+k. then k must be equal to

ans=1.

both the roots lie in (-1,1) so f(1).f(-1)>0 =>(a+c)^2 -b^2 >0

=>(a+c)^2>b^2 => a+c>b since a,b,c are integers the min value of a+c is b+1 so k=1

remember u asked the q before oneyeartogo told that f(1).f(-1)>0 for that i told that the condition is not sufficient yes but still the condition will be true though it is not sufficient.any way oneyeartogo made another mistake.but still his method was correct.and a,b,c are integers is an important point to be noted.

1.  should be an integer.