If $\alpha, \beta, \gamma$ are the roots of $x^3-2x^2+3x-4=0$,then the value of $\alpha^2\beta^2+\beta^2\gamma^2+\gamma^2\alpha^2$ is

Let $p$ and $q$ be two positive numbers such that $p + q = 2$ and $p^{4} + q^{4} = 272$. Then $p$ and $q$ are roots of the equation:

The two roots of the equation $x^3 - 9x^2 + 14x + 24 = 0$ are in the ratio $3 : 2$. Find the roots.

If $x^2-3x+2$ is a factor of $x^4-ax^2+b$,then the equation whose roots are $a$ and $b$ is

The equation $x^5-5x^3+5x^2-1=0$ has three equal roots. If $\alpha$ and $\beta$ are the other two roots of this equation,then $\alpha+\beta+\alpha\beta=$

If $\alpha_1, \alpha_2$ are the roots of $x^2+ax+1=0$ and $\alpha_3, \alpha_4$ are the roots of $x^2+bx+1=0$,then $(\alpha_1+\alpha_3)(\alpha_2+\alpha_3)(\alpha_1+\alpha_4)(\alpha_2+\alpha_4) = $