$p$ is a non-zero real number. If the equation whose roots are the squares of the roots of the equation $x^3 - px^2 + px - 1 = 0$ is identical to the given equation,then $p =$

If $\alpha, \beta$ and $\gamma$ are the roots of the equation $2x^3 - 3x^2 + 6x + 1 = 0$,then $\alpha^2 + \beta^2 + \gamma^2$ is equal to

If $\alpha$ and $\beta$ are the roots of $Ax^2 + Bx + C = 0$ and $\alpha^2$ and $\beta^2$ are the roots of $x^2 + px + q = 0$,then find the value of $p$.

$\alpha, \beta, \gamma$ are the roots of the equation $x^3-10 x^2+7 x+8=0$. Match the following and choose the correct answer.

$A. \alpha + \beta + \gamma$	$(1) -\frac{43}{4}$
$B. \alpha^2 + \beta^2 + \gamma^2$	$(2) -\frac{7}{8}$
$C. \frac{1}{\alpha} + \frac{1}{\beta} + \frac{1}{\gamma}$	$(3) 86$
$D. \frac{\alpha}{\beta \gamma} + \frac{\beta}{\gamma \alpha} + \frac{\gamma}{\alpha \beta}$	$(4) 0$
	$(5) 10$

If one root of the equation $x^2 + px + q = 0$ is the square of the other,then

Suppose that the equation $ax^2+bx+c=0$ has roots $\alpha$ and $\beta$,both of which are different from $\frac{1}{3}$. Then,an equation whose roots are $\frac{1}{3\alpha-1}$ and $\frac{1}{3\beta-1}$ is