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)

If $\alpha, \beta, \gamma, \delta$ are the roots of $x^4 - 100x^3 + 2x^2 + 4x + 10 = 0$,then $\frac{1}{\alpha} + \frac{1}{\beta} + \frac{1}{\gamma} + \frac{1}{\delta}$ is equal to:

If $\lambda \in R$ is such that the sum of the cubes of the roots of the equation $x^{2} + (2 - \lambda)x + (10 - \lambda) = 0$ is minimum,then the magnitude of the difference of the roots of this equation is

If the roots of the equations $ax^2 + bx + c = 0$ and $px^2 + qx + r = 0$ are $\alpha_1, \alpha_2$ and $\beta_1, \beta_2$ respectively,and the system of linear equations $\alpha_1y + \alpha_2z = 0$ and $\beta_1y + \beta_2z = 0$ has a non-zero solution,then which of the following is true?

If the roots of the quadratic equation $\frac{x - m}{mx + 1} = \frac{x + n}{nx + 1}$ are reciprocal to each other,then

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