If the roots of $x^2 - 7x + 6 = 0$ are $\alpha$ and $\beta$,then find the value of $\frac{1}{\alpha} + \frac{1}{\beta}$.

If $\alpha, \beta, \gamma$ are the roots of the equation $x^3-4x^2-9x+36=0$ such that $\alpha+\beta=0$,then $\alpha^2+2\beta^2+3\gamma^2=$

If the harmonic mean of the roots of the equation $\sqrt{2} x^2 - bx + (8 - 2\sqrt{5}) = 0$ is $4$,then the value of $b$ is

Let $\alpha$ and $\beta$ be the roots of the equation $p x^2 + q x + r = 0$,where $p \neq 0$. If $p, q, r$ are in $AP$ and $\frac{1}{\alpha} + \frac{1}{\beta} = 4$,then the value of $|\alpha - \beta|$ is

Suppose $\alpha, \beta, \gamma$ are roots of $x^3+x^2+2x+3=0$. If $f(x)=0$ is a cubic polynomial equation whose roots are $\alpha+\beta, \beta+\gamma, \gamma+\alpha$,then $f(x)$ is equal to

If $\alpha, \beta$ are the roots of the equation $x^2 - px + r = 0$ and $\alpha/2, 2\beta$ are the roots of the equation $x^2 - qx + r = 0$,then what is the value of $r$?