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

If $x$ be real, then the maximum value of $5 + 4x - 4{x^2}$ will be equal to

If $a < 0$ then the inequality $a{x^2} - 2x + 4 > 0$ has the solution represented by

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

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

If $3$ distinct real number $a$,$b$,$c$ satisfy $a^2(a + p) = b^2 (b + p) = c^2 (c + p)$ where $p \in R$, then value of $bc + ca + ab$ is