Quadratic equations and inequalities

9000020409

Level: 
B
One of the solutions of the quadratic equation \( x^{2} + bx - 10 = 0\) is \(x_{1} = 5\). Find the second solution \(x_{2}\) and the value of the coefficient \(b\).
\(x_{2} = -2\) and \(b = -3\)
\(x_{2} = -3\) and \(b = -2\)
\(x_{2} = 2\) and \(b = 3\)
\(x_{2} = 3\) and \(b = 2\)

9000021803

Level: 
B
Solve the following inequality. \[ (3x - 1)(2 - 4x) < 0 \]
\(x\in \left (-\infty ; \frac{1} {3}\right )\cup \left (\frac{1} {2};\infty \right )\)
\(x\in \left (\frac{1} {3}; \frac{1} {2}\right )\)
\(x\in \left (-\infty ; \frac{1} {2}\right )\)
\(x\in \left (\frac{1} {3};\infty \right )\)

9000022304

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