The cubic equation whose roots are thrice to each of the roots of $x^3+2x^2-4x+1=0$ is

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

If $p$ and $q$ are the roots of the equation $x^2 + pq = (p + 1)x$,then $q=$

If $\alpha, \beta, \gamma$ are the roots of the equation $x^3 + 2x - 5 = 0$ and the equation $x^3 + bx^2 + cx + d = 0$ has roots $2\alpha + 1, 2\beta + 1, 2\gamma + 1$,then the value of $|b + c + d|$ is (where $b, c, d$ are constants):

If the equation $x^{2}-cx+d=0$ has roots equal to the fourth powers of the roots of $x^{2}+ax+b=0,$ where $a^{2}>4b,$ then the roots of $x^{2}-4bx+2b^{2}-c=0$ will be

Let $\alpha, \beta$ be the roots of the equation $x^2-px+r=0$ and $\frac{\alpha}{2}, 2\beta$ be the roots of the equation $x^2-qx+r=0$. Then the value of $r$ is