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

Let $p$ and $q$ be real numbers such that $p \neq 0, p^3 \neq q$ and $p^3 \neq -q$. If $\alpha$ and $\beta$ are non-zero numbers satisfying $\alpha + \beta = -p$ and $\alpha^3 + \beta^3 = q$,then find the quadratic equation whose roots are $\frac{\alpha}{\beta}$ and $\frac{\beta}{\alpha}$.

If $\alpha, \beta$ and $\gamma$ are the roots of the equation $x^3-3x^2+x+5=0$,then $y=\Sigma \alpha^2+\alpha \beta \gamma$ satisfies the equation

If the sum of the squares of the reciprocals of the roots $\alpha$ and $\beta$ of the equation $3x^{2} + \lambda x - 1 = 0$ is $15$,then $6(\alpha^{3} + \beta^{3})^{2}$ is equal to

For the quadratic equation $2x^2 - 2(p - 2)x - p - 1 = 0$,what should be the value of $p$ such that the sum of the squares of its roots is minimized?

The values of $b$ and $c$ for which the identity $f(x+1)-f(x)=8x+3$ is satisfied,where $f(x)=bx^2+cx+d$,are