If one root of the equation $x^2 - 30x + p = 0$ is the square of the other root,then $p = \dots \dots \dots$

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

If $\alpha, \beta, \gamma$ are the roots of the equation $x^3-4x^2-9x+36=0$ such that $\alpha+\beta=0$,then $\alpha^2+2\beta^2+3\gamma^2=$

If $3$ distinct real numbers $a, b, c$ satisfy $a^2(a + p) = b^2(b + p) = c^2(c + p)$ where $p \in \mathbb{R}$,then the value of $bc + ca + ab$ is:

Let $\alpha$ and $\beta$ be the roots of $x^2+\sqrt{3}x-16=0$,and $\gamma$ and $\delta$ be the roots of $x^2+3x-1=0$. If $P_{n}=\alpha^{n}+\beta^{n}$ and $Q_{n}=\gamma^{n}+\delta^{n}$,then $\frac{P_{25}+\sqrt{3}P_{24}}{2P_{23}}+\frac{Q_{25}-Q_{23}}{Q_{24}}$ is equal to

Let $\alpha, \beta$ be the roots of the equation $x^2+2 \sqrt{2} x-1=0$. The quadratic equation,whose roots are $\alpha^4+\beta^4$ and $\frac{1}{10}(\alpha^6+\beta^6)$,is :