If $a, b$ and $c$ are the roots of $x^3+qx+r=0$,then $(a-b)^2+(b-c)^2+(c-a)^2=$ (in $q$)

If $\alpha, \beta, \gamma$ are the roots of $x^3+4x+1=0$,then the equation whose roots are $\frac{\alpha^2}{\beta+\gamma}, \frac{\beta^2}{\gamma+\alpha}, \frac{\gamma^2}{\alpha+\beta}$ is

If $\alpha$ and $\beta$ are the roots of $x^{2}-ax+b^{2}=0$,then $\alpha^{2}+\beta^{2}$ is equal to

Let $\alpha$ and $\beta$ be two distinct roots of the equation $x^3 + 3x^2 - 1 = 0$. The equation which has $(\alpha \beta)$ as its root is equal to

If $m_1$ and $m_2$ are the roots of the equation $x^2+(\sqrt{3}+2)x+(\sqrt{3}-1)=0$,then the area of the triangle formed by the lines $y=m_1x$,$y=m_2x$ and $y=c$ is:

Let $a, b, c$ be the roots of the equation $x^3 + 8x + 1 = 0$. Then the value of $\frac{bc}{(8b + 1)(8c + 1)} + \frac{ac}{(8a + 1)(8c + 1)} + \frac{ab}{(8a + 1)(8b + 1)}$ is equal to