Solve the equation $x^{2}+3x+9=0$.

The number of distinct quadratic equations $ax^2 + bx + c = 0$ with unequal real roots that can be formed by choosing the coefficients $a, b, c$ such that $a \neq b \neq c$ from the set $\{0, 1, 2, 4\}$ is:

Let $a, b, c \in \mathbb{R}$ and $\alpha, \beta$ be the real roots of the equation $ax^2 + bx + c = 0$. If $a < 0, b > 0, c > 0$ and $\alpha < \beta$,then:

If the quadratic equation $3x^2 + (2k + 1)x - 5k = 0$ has real and equal roots,then the value of $k$ such that $-\frac{1}{2} < k < 0$ is

If the resultant of two forces of magnitudes $P$ and $Q$ acting at a point at an angle of $60^\circ$ is $\sqrt{7}Q$,then $P/Q$ is

The number of real solutions of the equation $x|x+3|+|x-1|-2=0$ is