The given image shows the graph of a quadratic equation $y = ax^2 + bx + c$. Based on the graph,which of the following is true?

The number of real solutions of the equation $|x|^2 - 3|x| + 2 = 0$ is

The equation having the multiple root of the equation $x^4+4x^3-16x-16=0$ as its root is

What is the minimum value of the expression $x^2 + 4y^2 + 3z^2 - 2x - 12y - 6z + 14$?

Which of the following six statements are true about the cubic polynomial $P(x) = 2x^3 + x^2 + 3x - 2$?
$(i)$ It has exactly one positive real root.
$(ii)$ It has either one or three negative roots.
$(iii)$ It has a root between $0$ and $1$.
$(iv)$ It must have exactly two real roots.
$(v)$ It has a negative root between $-2$ and $-1$.
$(vi)$ It has no complex roots.

Let $-\frac{\pi}{6} < \theta < -\frac{\pi}{12}$. Suppose $\alpha_1$ and $\beta_1$ are the roots of the equation $x^2 - 2x \sec \theta + 1 = 0$ and $\alpha_2$ and $\beta_2$ are the roots of the equation $x^2 + 2x \tan \theta - 1 = 0$. If $\alpha_1 > \beta_1$ and $\alpha_2 > \beta_2$,then $\alpha_1 + \beta_2$ equals