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)

Two students were solving a quadratic equation in $x$. One student copied the constant term incorrectly and obtained the roots $3$ and $2$. The other student copied the constant term and the coefficient of $x^2$ correctly as $-6$ and $1$ respectively. What are the correct roots?

If $\alpha, \beta$ are the roots of the equation $x^2 + px + 1 = 0$ and $\gamma, \delta$ are the roots of the equation $x^2 + qx + 1 = 0$,then $q^2 - p^2 = \dots$

The value of $a$ for which one root of the quadratic equation $(a^2 - 5a + 3)x^2 + (3a - 1)x + 2 = 0$ is twice as large as the other,is

If the sum of the roots of the equation $ax^2 + bx + c = 0$ is equal to the sum of the squares of their roots,then:

If the sum of the squares of the roots of the equation $x^2 - (\sin \alpha - 2)x - (1 + \sin \alpha) = 0$ is least,then $\alpha$ is