If one of the roots of the equation $x^2 + ax + 3 = 0$ is $3$,and one of the roots of the equation $x^2 + ax + b = 0$ is three times the other root,then the value of $b$ is equal to

If $\alpha, \beta$, where $\alpha < \beta$, are the roots of the equation $\lambda x^{2} - (\lambda + 3)x + 3 = 0$ such that $\frac{1}{\alpha} - \frac{1}{\beta} = \frac{1}{3}$, then the sum of all possible values of $\lambda$ is:

If $\alpha$ and $\beta$ are the roots of the equation $2x^2 + 6x + k = 0$,then the maximum value of $\left[\frac{\alpha}{\beta} + \frac{\beta}{\alpha}\right]$ when $k < 0$ is (where $[\cdot]$ denotes the greatest integer function)

If the ratio of two roots of the equation $x^3 - 9x^2 + 14x + 24 = 0$ is $3 : 2$,find the roots of the equation.

If $\alpha, \beta, \gamma$ are the roots of the equation $x^3+p x^2+q x+r=0$,then $(\alpha+\beta)(\beta+\gamma)(\gamma+\alpha) =$

If $\alpha, \beta$ are the roots of $11 x^2+12 x-13=0$,then $\frac{1}{\alpha^2}+\frac{1}{\beta^2} = (\text{in } 2.54)?$ (approximately close to)