The roots of the equation $|x^2-x-6|=x+2$ are

If $\alpha$ and $\beta$ are the roots of $x^2+3(a+3)x-9a=0$ such that the roots are equal for different values of $a$ (where $\alpha > \beta$ is not applicable as roots are equal,but let $\alpha$ be the root for $a=-9$ and $\beta$ be the root for $a=-1$),then the minimum value of the expression $x^2+\alpha x-\beta$ is:

If $\sqrt{3x^2 - 7x - 30} + \sqrt{2x^2 - 7x - 5} = x + 5$,then $x = \dots$

$A$ building construction work can be completed by two masons $A$ and $B$ together in $22.5$ days. Mason $A$ alone can complete the work in $24$ days less than mason $B$ alone. Then mason $A$ alone will complete the work in: (in $days$)

Let $f(x)$ be a quadratic polynomial with $f(2)=10$ and $f(-2)=-2$. Then,the coefficient of $x$ in $f(x)$ is

If $S = {m \in \mathbb{R} : x^2 - 2(1 + 3m)x + 7(3 + 2m) = 0}$ has distinct roots $\}$,then the number of elements in $S$ is