If $\sin \alpha$ and $\cos \alpha$ are the roots of the equation $ax^2 + bx + c = 0$,then:

If $\alpha, \beta, \gamma$ are the roots of the equation $x^3+ax^2+bx+c=0$,then $\alpha^{-1}+\beta^{-1}+\gamma^{-1}$ is equal to

If $\alpha, \beta$ and $\gamma$ are the roots of the equation $x^3-6x^2+11x-6=0$,then $\Sigma \alpha^2 \beta + \Sigma \alpha \beta^2$ is equal to

Let $f(x) = x^3 - 2x + 2$. If real numbers $a, b, c$ are such that $|f(a)| + |f(b)| + |f(c)| = 0$,then the value of $f^2(a^2 + \frac{2}{a}) + f^2(b^2 + \frac{2}{b}) - f^2(c^2 + \frac{2}{c})$ is equal to:

If $\alpha$ and $\beta$ are the roots of the equation $x^2 + 6x + \lambda = 0$ and $3\alpha + 2\beta = -20$,then $\lambda = $

If $\alpha$ and $\beta$ are the roots of $x^{2}-px+1=0$ and $\gamma$ is a root of $x^{2}+px+1=0,$ then $(\alpha+\gamma)(\beta+\gamma)$ is