The range of `alpha` such that range of `f(x)=((x^(3)-3x+6)(x-alpha))/(2(x-alpha))` be always complete set `R` ,is

(x-alpha)^(2)+4(x-alpha)(-2)/(x-alpha)-3=0

If x in R then range of f(x)=(x^(2)+2x-3)/(2x^(2)+3x-9) is

If alpha is a real number such that alpha>1, then the range of the function f(x)=(a^(x)-a^(-|x|))/(alpha^(x)+alpha^(|x|)) is

If 1,1,alpha are the roots of x^(3)-6x^(3)+9x-4=0 then alpha=

If alpha,beta,1 are roots of x^(3)-2x^(2)-5x+6=0(alpha>1) then 3 alpha+beta=

If alpha is a roots equations 4x^(2)+2x-1=0 and f(x)=4x^(3)-3x+1, then 2(f(alpha)+alpha)

Find the range of (alpha,2+alpha) and ((3 alpha)/(2),a^(2)) lie on the opposite sides of the line 2x+3y=6.

If alpha is a root of the equation 4x^(2)+2x-1=0 and f(x)=4x^(2)-3x+1 , then 2(f(alpha)+(alpha)) is equal to

If alpha is a non-real root of x^(6)=1 then (alpha^(5)+alpha^(3)+alpha+1)/(alpha^(2)+1)=