Let `f(x)=a_(5)x^(5)+a_(4)x^(4)+a_(3)x^(3)+a_(2)x^(2)+a_(1)x, "where" a_(i),s` are real and f (x) = 0 has a positive root `alpha_(1).` Then

If f(x) = sum_(r=1)^(n)a_(r)|x|^(r) , where a_(i) s are real constants, then f(x) is

Consider (1+x+x^(2)) ^(n) = sum _(r=0)^(2n) a_(r) x^(r) , "where " a_(0),a_(1), a_(2),…a_(2n) are real numbers and n is a positive integer. The value of a_(2) is

If log_(e )((1+x)/(1-x))=a_(0)+a_(1)x+a_(2)x^(2)+…oo then a_(1), a_(3), a_(5) are in

If (1+2x+3x^(2))^(10)=a_(0)+a_(1)x+a_(2)x^(2)+a_(3)x^(3)+ . . .+a_(20)x^(20), then

If log (1-x+x^(2))=a_(1)x+a_(2)x^(2)+a_(3)x^(3)+… then a_(3)+a_(6)+a_(9)+.. is equal to

Consider (1 + x + x^(2))^(n) = sum_(r=0)^(n) a_(r) x^(r) , where a_(0), a_(1), a_(2),…, a_(2n) are real number and n is positive integer. The value of sum_(r=0)^(n-1) a_(r) is

Let (1 + x^(2))^(2) (1 + x)^(n) = a_(0) + a_(1) x + a_(2) x^(2) + … if a_(1),a_(2) " and " a_(3) are in A.P , the value of n is

Let f(x)=(a_(2k)x^(2k)+a_(2k-1)x^(2k-1)+...+a_(1)x+a_(0))/(b_(2k)x^(2k)+b_(2k-1)x^(2k-1)+...+b_(1)x+b_(0)) , where k is a positive integer, a_(i), b_(i) in R " and " a_(2k) ne 0, b_(2k) ne 0 such that b_(2k)x^(2k)+b_(2k-1)x^(2k-1)+...+b_(1)x+b_(0)=0 has no real roots, then

Differentiate |x|+a_(0)x^(n)+a_(1)x^(n-1)+a_(2)x^(n-1)+...+a_(n-1)x+a_(n)

If (x^(2)+x+1)/(1-x) = a_(0) + a_(1)x+a_(2)x^(2)+"…." , then sum_(r=1)^(50) a_(r) equal to