For the quadratic equation $ax^2 + bx + c = 0$,if $\alpha$ and $\beta$ are the roots,then $\frac{\alpha}{a\beta + b} + \frac{\beta}{a\alpha + b} = \dots$

The value of $p$ for which the sum of the squares of the roots of the equation $x^2 - (p + 3)x + (5p - 2) = 0$ assumes its least value is:

If $\alpha$ and $\beta$ are the roots of the equation $2x(2x+1)=1$,then $\beta$ is equal to

If $\alpha_1, \alpha_2, \alpha_3, \alpha_4, \alpha_5$ are the roots of $x^5-5 x^4+9 x^3-9 x^2+5 x-1=0$,then $\frac{1}{\alpha_1^2}+\frac{1}{\alpha_2^2}+\frac{1}{\alpha_3^2}+\frac{1}{\alpha_4^2}+\frac{1}{\alpha_5^2}=$

Find the sum of all possible values of $k$ for which the roots of the equation $x^2 + (k + 1)x + \lambda = 0$ are the square of each other.

Let $a$ and $b$ be two non-zero real numbers. If $p$ and $r$ are the roots of the equation $x^{2}-8ax+2a=0$ and $q$ and $s$ are the roots of the equation $x^{2}+12bx+6b=0$,such that $\frac{1}{p}, \frac{1}{q}, \frac{1}{r}, \frac{1}{s}$ are in $A$.$P$.,then $a^{-1}-b^{-1}$ is equal to $......$