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 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.

Let b be a non-zero real number. Suppose the quadratic equation 2x^2+bx+1/b = 0 has two distinct real roots. Then

If quadratic equation f(x)=x^(2)+ax+1=0 has two positive distinct roots then

Let S be the set of all alpha in R such that the equation, cos 2x + alpha sin x = 2alpha -7 has a solution. The S, is equal to

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

Find the value of K for which the quadratic equation kx^(2)+2x+1=0, has real and distinct root.

Show that there is no real number p for which the equation x^2 -3x + p =0 has two distinct roots in [0,1]