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 the sum of the roots of the quadratic equation $ax^2 + bx + c = 0$ is equal to the sum of the squares of their reciprocals,then $\frac{b^2}{ac} + \frac{bc}{a^2} = $

For the quadratic equation $4x^2 + 3x + 7 = 0$,if $\alpha$ and $\beta$ are the roots,then find the value of $1/\alpha + 1/\beta$.

If $\sin 2 \theta$ and $\cos 2 \theta$ are solutions of $x^2+bx-c=0$,then

If the roots of the equation $x^3+3px^2+3qx-8=0$ are in a geometric progression,then $\frac{q^3}{p^3}=$

Let $\alpha$ and $\beta$ be two real numbers such that $\alpha+\beta=1$ and $\alpha \beta=-1$. Let $p_{n}=\alpha^{n}+\beta^{n}$,$p_{n-1}=11$ and $p_{n+1}=29$ for some integer $n \geq 1$. Then,the value of $p_{n}^{2}$ is .... .