If $3p^2 = 5p + 2$ and $3q^2 = 5q + 2$,where $p \ne q$,then $pq$ is equal to

If $a+b+c=1$,$ab+bc+ca=2$ and $abc=3$,then the value of $a^{4}+b^{4}+c^{4}$ is equal to $...$

If the roots of the equation $x^2 + bx + ac = 0$ are $\alpha, \beta$ and the roots of the equation $x^2 + ax + bc = 0$ are $\alpha, \gamma$,then what are the values of $\alpha, \beta, \gamma$ respectively?

If the equation $x^{2}-cx+d=0$ has roots equal to the fourth powers of the roots of $x^{2}+ax+b=0,$ where $a^{2}>4b,$ then the roots of $x^{2}-4bx+2b^{2}-c=0$ will be

If $\alpha$ and $\beta$ are roots of $ax^2 + 2bx + c = 0$,then $\sqrt{\frac{\alpha}{\beta}} + \sqrt{\frac{\beta}{\alpha}}$ is equal to

Two roots of the cubic equation $x^3 + 3x^2 + kx + 12 = 0$ are real and unequal but have the same absolute value. Find the value of $k$.