Home
Class 11
MATHS
Let S be the set of all non-zero real nu...

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 ?` `(1/2,1/(sqrt(5)))` b. `(1/(sqrt(5)),0)` c. `(0,1/(sqrt(5)))` d. `(1/(sqrt(5)),1/2)`

Promotional Banner

Similar Questions

Explore conceptually related problems

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?

Number of integral values of a such that the quadratic equation x^(2)+a x+a+1=0 has integral roots is

The real roots of the quadratic equation x^(2)-x-1=0 are ___.

The set of all real x satisfying the inequality (3-|x|)/(4-|x|) ge 0 is

find the values k for which the quadratic equation 2x^2 + Kx +3=0 has two real equal roots

If the equation x^4- λx^2+9=0 has four real and distinct roots, then lamda lies in the interval

Let a ,\ b ,\ c be three non-zero real numbers such that the equation sqrt(3)\ acosx+2\ bsinx=c ,\ x in [-pi/2,pi/2] , has two distinct real roots alpha and beta with alpha+beta=pi/3 . Then, the value of b/a is _______.

The set of all real numbers x for which x^2-|x+2| +x gt 0 is

Find a quadratic equation whose product of roots x_1a n dx_2 is equal to 4 an satisfying the relation (x_1)/(x_1-1)+(x_2)/(x_2-1) =2.