Quadratic Equations and Inequalities

9000022304

Level: 
B
Find all the values of \(x\) at which the following expression attains nonnegative value. \[ x^{2} + x - 12 \]
\(x\in \left (-\infty ;-4\right ] \cup \left [ 3;\infty \right )\)
\(x\in \left [ -3;4\right ] \)
\(x\in \left [ -4;3\right ] \)
\(x\in \left (-\infty ;-4\right )\cup \left (3;\infty \right )\)
\(x\in \left (-\infty ;-3\right ] \cup \left [ 4;\infty \right )\)

9000022901

Level: 
C
An arrow has been shot at the angle \(60^{\circ }\) at the speed \(10\, \mathrm{m}\, \mathrm{s}^{-1}\). Find the time when the height equals to the horizontal distance from the take-off point. Hint: The position is given by the equations \(x = v_{0}t\cdot \cos \alpha \), \(y = v_{0}t\cdot \sin \alpha -\frac{1} {2}gt^{2}\). Use \(g = 10\, \mathrm{m}\, \mathrm{s}^{-2}\) as an acceleration of gravity.
\(\left (\sqrt{3} - 1\right )\, \mathrm{s}\)
\(\left (\sqrt{3} + 1\right )\, \mathrm{s}\)
\(\sqrt{3}\, \mathrm{s}\)
\(\left (\sqrt{2} - 1\right )\, \mathrm{s}\)
\(\left (\sqrt{2} + 1\right )\, \mathrm{s}\)