If $(1 - p)$ is a root of the quadratic equation $x^2 + px + (1 - p) = 0$,then its roots are:

Let $S = \{ \sin^2 2\theta : (\sin^4 \theta + \cos^4 \theta)x^2 + (\sin 2\theta)x + (\sin^6 \theta + \cos^6 \theta) = 0 \text{ has real roots} \}$. If $\alpha$ and $\beta$ are the smallest and largest elements of the set $S$,respectively,then $3((\alpha - 2)^2 + (\beta - 1)^2)$ equals:

If two roots of the equation $x^3 - 3x + 2 = 0$ are the same,then the roots are:

The number of pairs $(a, b)$ of real numbers such that whenever $\alpha$ is a root of the equation $x^{2}+ax+b=0$,$\alpha^{2}-2$ is also a root of this equation,is:

Let $S$ be the set of all possible integral values of $\lambda$ in the interval $(-3, 7)$ for which the roots of the quadratic equation $\lambda x^2 + 13x + 7 = 0$ are all rational numbers. Then the sum of the elements in $S$ is

If the equation $x^2 - m(2x - 8) - 15 = 0$ has equal roots,then $m = ......$