Quadratic equations and inequalities

1003047001

Level: 
A
We are given the equation \( 2x^2+10x=8x+2x^2 \). Decide which of the following equations has the different set of roots than the given equation has, i.e. choose the equation which is not equivalent to the given equation.
\( 2x+10=8+2x \)
\( 10x=8x \)
\( 2x^2+2x=2x^2 \)
\( x^2+5x=4x+x^2 \)

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. \[ \left (x + 1\right )\left (4 + x\right ) \]
\(\left [ -4;-1\right ] \)
\(\left (-\infty ;-4\right ] \cup \left [ -1;\infty \right )\)
\(\left (-4;-1\right )\)
\(\left (-\infty ;-4\right )\cup \left (-1;\infty \right )\)

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.
\(\left (5x + 3\right )\left (1 - 6x\right ) < 0\)
\(\left (5x - 3\right )\left (6x + 1\right ) < 0\)
\(\left (5x + 3\right )\left (1 - 6x\right ) > 0\)
\(\left (5x - 3\right )\left (6x + 1\right ) > 0\)