Let S be the set of all real values of `alpha` such that the second degree equation in x, `x^2-2alphax+alpha^2-2alpha-1=0` has two distinct real roots p and q satisfying condition `1/2((p-q)^2-2)/((p+q)+2)` is an integer, then number of elements in set S, is

Let S be the set of all real values of alpha such that the second degree equation in x,x^(2)-2 alpha x+alpha^(2)-2 alpha-1=0 has two distinct real roots p and q satisfying condition (1)/(2)((p-q)^(2)-2)/((p+q)+2) is an integer,then number of elements in set S, is

Let S be the set of all non-zero real numbers alpha such that the quadratic equation alphax^2-x+alpha=0 has two distinct real roots x_1 and x_2 satisfying the inequality abs(x_1-x_2)lt1 . Which of the following intervals is (are) a subset(s) of S ?

Let S be the set of all non-zero numbers alpha such that the quadratic equation alphax^2-x+alpha=0 has two distinct real roots x_1, and x_2 satisfying the inequality |x_1-x_2|lt1 which of the following intervals is(are) a subset of S?

Let S be the set of all non-zero numbers alpha such that the quadratic equation alphax^2-x+alpha=0 has two distinct real roots x_1, and x_2 satisfying the inequality |x_1-x_2|lt1 which of the following intervals is(are) a subset of S?

Let S be the set of all non-zero numbers alpha such that the quadratic equation alpha x^(2)-x+alpha=0 has two distinct real roots x_(1), and x_(2) satisfying the inequality |x_(1)-x_(2)|<1 which of the following intervals is(are) a subset of S?

Let S be the set of all non-zero real numbers such that the quadratic equation alphax^2-x+alpha=0 has two distinct real roots x_1a n dx_2 satisfying the inequality |x_1-x_2|<1. Which of the following intervals is (are) a subset (s) of S ?

Let S be the set of all non-zero real numbers such that the quadratic equation alphax^2-x+alpha=0 has two distinct real roots x_1a n dx_2 satisfying the inequality |x_1-x_2|<1. Which of the following intervals is (are) a subset (s) of S ?

Let S be the set of the non zero real numbers alpha such that the quadratic equation alphax^(2)-x+alpha=0 has two distinct real roots x_(1)andx_(2) satisfying the inequlity |x_(1)-x_(2)|lt1 . Which of the following intervals is (are) a subset (s) of s?

Let S be the set of all non-zero real numbers such that the quadratic equation alpha x^(2)-x+alpha=0 has two distinct real roots x_(1) and x_(2) satisfying the inequality |x_(1)-x_(2)|<1. Which of the following intervals is (are) a subset (s) of S?(-(1)/(2),(1)/(sqrt(5))) b.(-(1)/(sqrt(5)),0) c.(0,(1)/(sqrt(5))) d.((1)/(sqrt(5)),(1)/(2)) b.