$A$ two-digit number is four times the sum of its digits and three times the product of its digits. The number is:

If the roots of the equation $(p-3)x^2 + 2(p-3)x + 2p-5 = 0$ are real and distinct for $\alpha < p < \beta$ and $(\beta - \alpha)$ is maximum,then the extreme value of the quadratic expression $-(\alpha + \beta)x^2 + \alpha \beta x + (\alpha - \beta)$ is

If $f(x)$ is a quadratic expression such that $f(1) + f(2) = 0$,and $-1$ is a root of $f(x) = 0$,then the other root of $f(x) = 0$ is

If the resultant of two forces of magnitudes $P$ and $Q$ acting at a point at an angle of $60^\circ$ is $\sqrt{7}Q$,then $P/Q$ is

The roots of the equation $x^3-3x-2=0$ are

The roots of the equation $(x-a)(x-a-1)+(x-a-1)(x-a-2)+(x-a)(x-a-2)=0$ for $a \in R$ are always: