If the quadratic equations $3 x^2-7 x+2=0$ and $k x^2+7 x-3=0$ have a common root then the positive value of $k$ is

If the roots of $x^3+a x^2+b x+c=0$ are in arithmetic progression with common difference 1 , then

If $\alpha, \beta, \gamma$ are the roots of the equation $x^3+3 x^2-x-3=0$, then $\left(1+\alpha^2\right)\left(1+\beta^2\right)\left(1+\gamma^2\right)=$

If $\alpha$ and $\beta$ are the real roots of the equation $\sqrt{\frac{5 x}{x-2}}+\sqrt{\frac{x-2}{5 x}}=\frac{29}{10}$ and $\alpha>\beta$, then $\sqrt{\alpha^2-11^4 \beta^2}=$