If $\alpha$ is a multiple root of the equation $x^5-6x^4+11x^3-2x^2-12x+8=0$,then $3\alpha^2-2\alpha+1=$

If $\alpha, \beta, \gamma, \delta$ are the roots of the equation $x^4-4x^3+3x^2+2x-2=0$ such that $\alpha$ and $\beta$ are integers and $\gamma, \delta$ are irrational numbers,then $\alpha+2\beta+\gamma^2+\delta^2=$

What are the roots of the given equation $(p - q)x^2 + (q - r)x + (r - p) = 0$?

For which interval of values of $a$ will the equation $3x^2 + 2(a^2 + 1)x + (a^2 - 3a + 2) = 0$ have roots of opposite signs?

Let $b$ be a non-zero real number. Suppose the quadratic equation $2x^2 + bx + \frac{1}{b} = 0$ has two distinct real roots. Then:

If $\alpha$ and $\beta$ $(\alpha < \beta)$ are the roots of the equation $(-2+\sqrt{3})(|\sqrt{x}-3|) + (x-6\sqrt{x}) + (9-2\sqrt{3}) = 0$,$x \ge 0$,then $\sqrt{\frac{\beta}{\alpha}} + \sqrt{\alpha\beta}$ is equal to: