Quadratic Equat...

If $$\alpha$$ and $$\beta$$ are roots of the equation $$x^2 + \sin \theta . 2 \sin \theta = 0 $$ then $$\dfrac{\alpha^{12} + \beta^{12}}{(\alpha^{-12} + \beta^{-12})(\alpha - \beta)^{24}}$$ is equal to 

Which one of the following is the quadratic equation?

The integral values of $$ m $$ for which the roots of the equation $$ m x^{2}+(2 m-1) x+(m-2)=0 $$ are rational are given by the expression [where $$ n$$ is integer ] 

Which of the following is not a quadratic equation?

Which of the following is a quadratic equation?

Which among the below are quadratic equations?

Discriminant of quadratic equation $$3\sqrt 3x^2+10x+\sqrt 3=0$$

All solutions of the equation $$\displaystyle 4x^2 - 40x + 51  = 0$$ lie in the interval 

The values of $$a$$ for which both the roots of the equation $$(a-6)x^2=a(x-3)$$  are positive and are given by

The roots of $$(x-a)(x-c)+k(x-b)(x-d)=0$$ are real and distinct for all real $$k$$ if