When the roots of $x^3+\alpha x^2+\beta x+6=0$ are increased by 1 , if one of the resultant values is the least root of $x^4-6 x^3+11 x^2-6 x=0$, then

Let ' $a$ ' be a non-zero real number. If the equation whose roots are the squares of the roots of the cubic equation $x^3-a x^2+a x-1=0$ is identical with this cubic equation, then ' $a$ ' =

If $(2 k-1) x^2-2(3 k-2) x+4 k>0$ for every $x \in R$, then the sum of all possible integral values of $k$ is

If $\alpha$ is a repeated root of multiplicity 2 of the equation $18 x^3-33 x^2+20 x-4=0$, then