If the roots of the given equation $2x^2 + 3(\lambda - 2)x + \lambda + 4 = 0$ are equal in magnitude but opposite in sign,then $\lambda = $

If $\alpha$ and $\beta$ are the roots of the equation $x^2 - 4x + 1 = 0$,the value of $\alpha^3 + \beta^3$ is:

If $\alpha, \beta$ are the roots of the equation $x^2+bx+c=0$ satisfying the conditions $\alpha+\beta=5$ and $\alpha^3+\beta^3=60$,then $3c+2=$ (in $b$)

Which equation has roots that are the squares of the roots of the equation $ax^2 + bx + c = 0$?

If $\alpha, \beta$ are the roots of $x^2-5 \gamma x-6 \delta=0$ and $\gamma, \delta$ are the roots of $x^2-5 \alpha x-6 \beta=0$,then $\alpha+\beta+\gamma+\delta=$

If $\alpha, \beta$ are the roots of $x^2 - x + p = 0$ and $\gamma, \delta$ are the roots of $x^2 - 4x + q = 0$,and if $\alpha, \beta, \gamma, \delta$ are in a geometric progression,then the values of $p$ and $q$ are respectively: