The sum of the squares of all the roots of the equation $x^2+|2x-3|-4=0$ is:

$A$ student,while solving a quadratic equation in $x$,copied its constant term incorrectly and obtained the roots as $5$ and $9$. Another student copied the constant term and the coefficient of $x^2$ of the same equation correctly as $12$ and $4$ respectively. If $s$,$p$,and $\Delta$ denote the sum of the roots,the product of the roots,and the discriminant of the correct equation respectively,then find the value of $\frac{\Delta}{3p+s}$.

If $x$ is real,then the maximum and minimum values of $\frac{x^2+14x+9}{x^2+2x+3}$ are respectively

The adjoining figure shows the graph of $y = a{x^2} + bx + c$. Then:

If $\alpha, \beta$ are the roots of the equation $x^2 - px + q = 0$,then the quadratic equation whose roots are $(\alpha^2 - \beta^2)(\alpha^3 - \beta^3)$ and $\alpha^3\beta^2 + \alpha^2\beta^3$ is (where $S = p[p^4 - 5p^2q + 5q^2]$ and $P = p^2q^2(p^4 - 5p^2q + 4q^2)$).

If $a^2+b^2+c^2=1$,where $a, b, c \in \mathbb{R}$,then the set of extreme values of $ab+bc+ca$ is