The smallest value of ${x^2} – 3x + 3$ in the interval $( – 3,\,3/2)$ is

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

Two distinct polynomials $f(x)$ and $g(x)$ are defined as follows:

$f(x)=x^2+a x+2 ; g(x)=x^2+2 x+a$.If the equations $f(x)=0$ and $g(x)=0$ have a common root, then the sum of the roots of the equation $f(x)+g(x)=0$ is

If $\alpha , \beta $ are the roots of the equation $x^2 – 2x + 4 = 0$ , then the value of $\alpha ^n +\beta ^n$ is

If $\alpha , \beta , \gamma $ are roots of equation ${x^3} + a{x^2} + bx + c = 0$, then ${\alpha ^{ – 1}} + {\beta ^{ – 1}} + {\gamma ^{ – 1}} = $