If $x+\frac{1}{x}=a, x^2+\frac{1}{x^3}=b$, then $x^3+\frac{1}{x^2}$ is

The number of real roots of the polynomial equation $x^4-x^2+2 x-1=0$ is

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

The set of all $a \in R$ for which the equation $x | x -1|+| x +2|+a=0$ has exactly one real root is:

The sum of the cubes of all the roots of the equation $x^{4}-3 x^{3}-2 x^{2}+3 x+1=10$ is

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