Quadratic Equations and Inequalities

9000022304

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

9000020408

Level: 
A
Which of the given equations have at least one root the same? \[ \begin{aligned} x^{2} + 8x + 15 & = 0 &\text{(1)} \\x^{2} - 8x + 15 & = 0 &\text{(2)} \\x^{2} +\phantom{ 8}x - 12 & = 0 &\text{(3)} \\x^{2} - 2x -\phantom{ 1}8 & = 0 &\text{(4)} \\\end{aligned}\]
equations (2) and (3)
equations (1) and (3)
equations (2) and (4)
Such a pair does not exist.