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

Let $p$ and $q$ be two real numbers such that $p+q=$ 3 and $p^{4}+q^{4}=369$. Then $\left(\frac{1}{p}+\frac{1}{q}\right)^{-2}$ is equal to

If for a posiive integer $n$ , the quadratic equation, $x\left( {x + 1} \right) + \left( {x + 1} \right)\left( {x + 2} \right) + .\;.\;.\; + \left( {x + \overline {n - 1} } \right)\left( {x + n} \right) = 10n$ has two consecutive integral solutions, then $n$ is equal to:

If $x$ is real, the expression $\frac{{x + 2}}{{2{x^2} + 3x + 6}}$ takes all value in the interval

The number of the real roots of the equation $(x+1)^{2}+|x-5|=\frac{27}{4}$ is ....... .

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