If `alpha` is the only real root of `x^3+bx^2+cx+1=0(bltc)` , then the value of `|[alpha]|` is (where,[.] represents the greatest integer function) .

If alpha is an integer satisfying |alpha|lt=4-|[x]|, where x is a real number for which 2xtan^(-1)x is greater than or equal to ln(1+x^2), then the number of maximum possible values of alpha (where [.] represents the greatest integer function) is_____

If alpha is an integer satisfying |alpha|lt=4-|[x]|, where x is a real number for which 2xtan^(-1)x is greater than or equal to ln(1+x^2), then the number of maximum possible values of alpha (where [.] represents the greatest integer function) is_____

If alpha is an integer satisfying |alpha|lt=4-|[x]|, where x is a real number for which 2xtan^(-1)x is greater than or equal to ln(1+x^2), then the number of maximum possible values of alpha (where [.] represents the greatest integer function) is_____

If the greatest value of sin^2alpha is a/(256), then the value of [a/(10)] is (where [.] denotes greatest integer function)

if alpha is a real root of 2x^3-3x^2 + 6x + 6 = 0, then find [alpha ] where [] denotes the greatest integer function.

If alpha is an integer satisfying |a|le4-|[x]| , where x is a real number for which 2xtan^(-1)x is greater than or equal to In (1+x^(2)) , then the number of maximum possible values of a (where[.] represents the greatest integer function) is

If alpha,beta,gamma be the roots of ax^3+bx^2+cx+d=0 then find the value of sum 1/alpha .

If alpha is an integer satisfying | alpha|<=4-|[x]| where x is a real number for which 2x tan^(-1)x is greater than or equal to ln(1+x^(2)), then the number of maximum possible values of alpha (where I.l represents the greatest integer function is

If alpha is the only real root of the equation x^3 + bx^2 + cx + 1 = 0 (b < c) , then the value of tan^-1 alpha+ tan^-1 (alpha^-1) is equal to :

If alpha is the only real root of the equation x^3 + bx^2 + cx + 1 = 0 (b < c) , then the value of tan^-1 alpha+ tan^-1 (alpha^-1) is equal to :