If $x$ is a real number,what is the maximum value of $\frac{3x^2 + 9x + 17}{3x^2 + 9x + 7}$?

Let $\alpha$ and $\beta$ be the roots of the equation $(x - a)(x - b) = c$,where $c \neq 0$. What are the roots of the equation $(x - \alpha)(x - \beta) + c = 0$?

Let $P(x)$ be a polynomial, which when divided by $(x-3)$ and $(x-5)$ leaves remainders $10$ and $6$, respectively. If the polynomial is divided by $(x-3)(x-5)$, then the remainder is

The product and sum of the roots of the equation $|x|^2 - 5|x| - 24 = 0$ are respectively:

What is the sum of all natural numbers $n$ such that the product of the digits of $n$ (in base $10$) is equal to $n^2-10n-36$?

If the set of all $a \in R - \{1\}$,for which the roots of the equation $(1-a)x^2 + 2(a-3)x + 9 = 0$ are positive,is $(-\infty, -\alpha] \cup [\beta, \gamma)$,then $2\alpha + \beta + \gamma$ is equal to . . . . . . .