Quadratic Equations and Inequalities

9000034905

Level: 
B
The solution set of one of the following quadratic inequalities is the interval \(\left [ -\frac{7} {6}, \frac{3} {4}\right ] \). Determine this inequality.
\(\left (x + \frac{7} {6}\right )\left (x -\frac{3} {4}\right )\leq 0\)
\(\left (x + \frac{7} {6}\right )\left (x -\frac{3} {4}\right )\geq 0\)
\(\left (x -\frac{7} {6}\right )\left (x + \frac{3} {4}\right )\geq 0\)
\(\left (x -\frac{7} {6}\right )\left (x + \frac{3} {4}\right )\leq 0\)

9000034906

Level: 
B
The solution set of one of the following quadratic inequalities is \(\left (-\infty ,-\frac{3} {5}\right )\cup \left (\frac{1} {6},\infty \right )\). Determine this inequality.
\(\left (5x + 3\right )\left (1 - 6x\right ) < 0\)
\(\left (5x - 3\right )\left (6x + 1\right ) < 0\)
\(\left (5x + 3\right )\left (1 - 6x\right ) > 0\)
\(\left (5x - 3\right )\left (6x + 1\right ) > 0\)

9000034907

Level: 
B
Find all \(x\in \mathbb{R}\) for which the following expression takes nonnegative values. \[ -2\left (x - 3\right )\left (2 - x\right ) \]
\(\left (-\infty ,2\right ] \cup \left [ 3,\infty \right )\)
\(\left [ 2,3\right ] \)
\(\left (2,3\right )\)
\(\left (-\infty ,2\right )\cup \left (3,\infty \right )\)

9000034908

Level: 
B
Find all \(x\in \mathbb{R}\) for which the following expression is nonpositive. \[ \left (x + 1\right )\left (4 + x\right ) \]
\(\left [ -4,-1\right ] \)
\(\left (-\infty ,-4\right ] \cup \left [ -1,\infty \right )\)
\(\left (-4,-1\right )\)
\(\left (-\infty ,-4\right )\cup \left (-1,\infty \right )\)