Assume that $\alpha, \beta, \gamma$ are the roots of $2x^3+5x^2+5x+2=0$. For $h \in R$,if $\alpha+h, \beta+h, \gamma+h$ are roots of $a(h)x^3+b(h)x^2+c(h)x+d(h)=0$,then:

The value of $a$ $(a \ge 3)$ for which the sum of the cubes of the roots of $x^2 - (a - 2)x + (a - 3) = 0$ assumes the least value is:

If one root of the equation $x^2 - 30x + p = 0$ is the square of the other root,then $p = \dots \dots \dots$

If the roots of the equations $x^2 - bx + c = 0$ and $x^2 - cx + b = 0$ differ by the same quantity,then $b + c$ is equal to

Let $p$ and $q$ be real numbers such that $p \neq 0, p^3 \neq q$ and $p^3 \neq -q$. If $\alpha$ and $\beta$ are non-zero numbers satisfying $\alpha + \beta = -p$ and $\alpha^3 + \beta^3 = q$,then find the quadratic equation whose roots are $\frac{\alpha}{\beta}$ and $\frac{\beta}{\alpha}$.

If $\alpha$ and $\beta$ are the roots of the equation $ax^2+bx+c=0$,then the equation whose roots are $\alpha+\beta$ and $\frac{1}{\alpha}+\frac{1}{\beta}$ is