The minimum value of the sum of the squares of the roots of $x^{2}+(3-a)x+1=2a$ is:

If the harmonic mean between the roots of $(5+\sqrt{2}) x^2-b x+(8+2 \sqrt{5})=0$ is $4$,then the value of $b$ is

Let $a$ be a non-zero real number. If the equation whose roots are the squares of the roots of the cubic equation $x^3 - ax^2 + ax - 1 = 0$ is identical to the original cubic equation,then $a =$

If $\alpha, \beta, \gamma$ are the roots of the equation $x^3-5x^2-2x+24=0$,then $\frac{\beta\gamma}{\alpha}+\frac{\gamma\alpha}{\beta}+\frac{\alpha\beta}{\gamma}=$

If $\alpha, \beta, \gamma, \delta$ are in geometric progression,where $\alpha, \beta$ are the roots of the equation $ax^2 + 2bx + c = 0$ and $\gamma, \delta$ are the roots of the equation $px^2 + 2qx + r = 0$,then:

The roots of the equation $x^2 + ax + b = 0$ are $p$ and $q$. Then the equation whose roots are $p^2q$ and $pq^2$ will be: