If the difference between the roots of the equation $x^2 + px + q = 0$ is $1$,then:

If $\alpha$ and $\beta$ are the roots of the equation $ax^2+bx+c=0$,then the equation whose roots are $\alpha+\beta$ and $\frac{1}{\alpha}+\frac{1}{\beta}$ is

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

If one root of $x^2 - x - k = 0$ is the square of the other,then $k =$

The difference between two roots of the equation $x^3-13x^2+15x+189=0$ is $2$. Then the roots of the equation are:

If the roots of the equation $x^2 - 5x + 16 = 0$ are $\alpha, \beta$ and the roots of the equation $x^2 + px + q = 0$ are $\alpha^2 + \beta^2$ and $\frac{\alpha \beta}{2}$,then: