If `alpha` and `beta(alpha lt beta)` are the roots of the equation `x^(2)+bx+c=0` where `c lt 0ltb`, then

If alpha and beta (alpha lt beta) are the roots of the equation x^(2) + bx + c = 0 , where c lt 0 lt b , then

If alpha and beta ( alpha'<'beta') are the roots of the equation x^2+b x+c=0, where c<0

If alpha beta( alpha lt beta) are two distinct roots of the equation. ax^(2)+bx+c=0 , then

Statement I: x^2-5x+6<0 if 2 < x < 3 Statement II: If alpha and beta, (alpha < beta) are the roots of the equation ax^2+bx+c=0 and alpha < x < beta then ax^2+bx+c and a have opposite signs

If alpha, beta (alpha lt beta) are the roots of the equation 6x^(2) + 11x + 3 = 0 , then which of the following are real ?

If alpha,beta are the roots of the equation ax^(2)+bx+c=0 then log(a-bx+cx^(2)) is equal to

If alpha and beta are the roots of the equation ax ^(2) + bx + c=0,a,b, c in R , alpha ne 0 then which is (are) correct:

If alpha and beta are the roots of the equation x^(2)+alpha x+beta=0 such that alpha ne beta , then the number of integral values of x satisfying ||x-beta|-alpha|lt1 is

If alpha and beta are the roots of the equation ax^2 + bx +c =0 (a != 0; a, b,c being different), then (1+ alpha + alpha^2) (1+ beta+ beta^2) =

If alpha and beta are the roots of the equation x^(2)+x+c=0 such that alpha+beta, alpha^(2)+beta^(2) and alpha^(3)+beta^(3) are in arithmetic progression, then c is equal to