If $\alpha$ and $\beta$ are the roots of $x^2+7x+3=0$ and $\frac{2\alpha}{3-4\alpha}, \frac{2\beta}{3-4\beta}$ are the roots of $ax^2+bx+c=0$ and $GCD(a, b, c) = 1$,then $a+b+c=$

If the sum of the roots of the equation $ax^2 + bx + c = 0$ is equal to the sum of the reciprocals of their squares,then $bc^2, ca^2, ab^2$ will be in

If $\alpha, \beta, \gamma$ are the roots of the equation $x^3 + 5x^2 - 7x - 1 = 0$,then find the equation whose roots are $\alpha\beta, \beta\gamma, \gamma\alpha$.

For what value of $a$, the sum of the squares of the roots of the equation $x^2-(a-2)x-a+1=0$ will have the least value?

If $\alpha, \beta, \gamma$ are the roots of the equation $x^3-6x^2+11x-6=0$ and if $a=\alpha^2+\beta^2+\gamma^2$,$b=\alpha\beta+\beta\gamma+\gamma\alpha$ and $c=(\alpha+\beta)(\beta+\gamma)(\gamma+\alpha)$,then the correct inequality among the following is

If $\alpha, \beta$ are the roots of the equation $x^2 - px + r = 0$ and $\alpha/2, 2\beta$ are the roots of the equation $x^2 - qx + r = 0$,then what is the value of $r$?