The sum of the roots of the equation $x^2 + |2x - 3| - 4 = 0$ is:

Let $p, q, r \in \mathbb{R}$ and $r > p > 0$. If the quadratic equation $px^2 + qx + r = 0$ has two complex roots $\alpha$ and $\beta$,then what is the value of $|\alpha| + |\beta|$?

Let $S = \{ \sin^2 2\theta : (\sin^4 \theta + \cos^4 \theta)x^2 + (\sin 2\theta)x + (\sin^6 \theta + \cos^6 \theta) = 0 \text{ has real roots} \}$. If $\alpha$ and $\beta$ are the smallest and largest elements of the set $S$,respectively,then $3((\alpha - 2)^2 + (\beta - 1)^2)$ equals:

Let $\alpha, \beta$ be the roots of the quadratic equation $12x^{2}-20x+3\lambda=0$,where $\lambda \in \mathbb{Z}$. If $\frac{1}{2} \le |\beta-\alpha| \le \frac{3}{2}$,then the sum of all possible values of $\lambda$ is:

If the graph of $y = ax^3 + bx^2 + cx + d$ is symmetric about the line $x = k$,then:

The number of real values of $x$ for which the equality $|3x^2 + 12x + 6| = 5x + 16$ holds is: