Write a general polynomial `q(z)` of degree n with coefficients that are `b_(0),b_(1),b_(2), . . .. N_(n)`,
What are the conditions on `b_(0),b_(1),b_(2), . . .. B_(n)` ?

The sequence a_(1),a_(2),a_(3),".......," is a geometric sequence with common ratio r. The sequence b_(1),b_(2),b_(3),".......," is also a geometric sequence. If b_(1)=1,b_(2)=root4(7)-root4(28)+1,a_(1)=root4(28)" and "sum_(n=1)^(oo)(1)/(a_(n))=sum_(n=1)^(oo)(1)/(b_(n)) , then the value of (1+r^(2)+r^(4)) is

Find the value of n so that (a^(n+1)+b^(n+1))/(a^n+b^n) may be the geometric mean between a and b.

If the arithmetic mean of a_(1),a_(2),a_(3),"........"a_(n) is a and b_(1),b_(2),b_(3),"........"b_(n) have the arithmetic mean b and a_(i)+b_(i)=1 for i=1,2,3,"……."n, prove that sum_(i=1)^(n)(a_(i)-a)^(2)+sum_(i=1)^(n)a_(i)b_(i)=nab .

Find the value of n so that (a^(n+1)+b^(n+1))/(a^(n)+b^n) may be the geometric mean between a and b.

Sum of the power of a and b in expansion (a+b)^n is n .

If a, b, c, d are in G.P, prove that (a^n + b^n), (b^n + c^n), (c^n + d^n) are in G.P.

Show that two lines a_(1) x + b_(14) y + c_(1) = 0 and a_(2) x + b_(2) y + c_(2) = 0 , where b_(1) , b_(2) ne 0 are Perpendicular if a_(1) a_(2) + b_(1) b_(2) =0 .

If the coordinates (x, y, z) of the point S which is equidistant from the points O(0, 0, 0), A(n^(5), 0, 0), B(0, n^(4), 0), C(0, 0, n) obey the relation 2(x+y+z)+1=0 . If ninZ , then |n|= _____( |*| is the mudulus function).