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 and beta are the roots of the equation x^(2) + bx + c = 0 , then the roots of the equation cx^(2) -b x + 1=0 are

If alpha is a real root of the cubic equation ax^(3)+bx^(2)+bx+a=0, then the value of lim_(x rarr(1)/(a))(tan(ax^(3)+bx^(2)+bx+a))/((alpha x-1)) is

If the roots of the equation x^(3) + bx^(2) + cx - 1 = 0 form an increasing G.P., then b belongs to the interval

If the roots of the equation x^(3) + bx^(2) + cx - 1 = 0 form an increasing G.P., then b belongs to the interval

Statement-1: If alpha and beta are real roots of the quadratic equations ax^(2) + bx + c = 0 and -ax^(2) + bx + c = 0 , then (a)/(2) x^(2) + bx + c = 0 has a real root between alpha and beta Statement-2: If f(x) is a real polynomial and x_(1), x_(2) in R such that f(x_(1)) f_(x_(2)) lt 0 , then f(x) = 0 has at leat one real root between x_(1) and x_(2) .

Statement-1: If alpha and beta are real roots of the quadratic equations ax^(2) + bx + c = 0 and -ax^(2) + bx + c = 0 , then (a)/(2) x^(2) + bx + c = 0 has a real root between alpha and beta Statement-2: If f(x) is a real polynomial and x_(1), x_(2) in R such that f(x_(1)) f_(x_(2)) lt 0 , then f(x) = 0 has at leat one real root between x_(1) and x_(2) .

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 the roots of the equation x^(3) + bx^(2) + cx + d = 0 are in arithmetic progression, then b, c and d satisfy the relation

If the roots of the equation x^(3) + bx^(2) + cx + d = 0 are in arithmetic progression, then b, c and d satisfy the relation