If $\alpha, \beta, \gamma$ are the roots of the equation $2x^3-5x^2+4x-3=0$,then $\sum \alpha \beta(\alpha+\beta)=$

The cubic equation whose roots are the squares of the roots of the equation $12x^3-20x^2+x+3=0$ is

For what value of $m$ will one root of $x^2 - 3x + 2m = 0$ be double one root of $x^2 - x + m = 0$?

If the sum of the roots of the quadratic equation $ax^2 + bx + c = 0$ is equal to the sum of the squares of their reciprocals,then $a/c, b/a, c/b$ are in

If one root of the quadratic equation $ax^2 + bx + c = 0$ is equal to the $n^{th}$ power of the other root,then the value of $(ac^n)^{\frac{1}{n+1}} + (a^nc)^{\frac{1}{n+1}} = $

If $a, -a, b$ are the roots of $x^{3}-5x^{2}-x+5=0$,then $b$ is a root of