9000022809
Level:
B
Find the solution set of the following quadratic inequality.
\[
4x^{2} + 4x + 1 < 0
\]
\(\emptyset \)
\(\mathbb{R}\)
\(\left \{\frac{1}
{2}\right \}\)
\(\left \{-\frac{1}
{2}\right \}\)
Quadratic equations and inequalities
9000022810
Level:
B
Find the solution set of the following quadratic inequality.
\[
-x^{2} + 2x + 3 > 0
\]
\((-1;3)\)
\((-\infty ;-1)\)
\((-\infty ;-1)\cup (3;\infty )\)
\((3;\infty )\)
9000022807
Level:
B
Complete the following statement: Quadratic inequality
\[
2x^{2} - 3x + 4 > x^{2} + 2x - 2
\]
is satisfied if and only if
\(x\in (-\infty ;2)\cup (3;\infty )\).
\(x\in (2;3)\).
\(x\in (-\infty ;-2)\cup (-3;\infty )\).
\(x\in (-2;-3)\).
9000022808
Level:
B
Find all the real values of \(x\)
which ensure that the following expression is negative.
\[
-x^{2} + 4x - 4
\]
\(x\in \mathbb{R}\setminus \{2\}\)
none \(x\)
with this property
\(x = 2\)
\(x\in \mathbb{R}\)
9000022304
Level:
B
Find all the values of \(x\)
at which the following expression attains nonnegative value.
\[
x^{2} + x - 12
\]
\(x\in \left (-\infty ;-4\right ] \cup \left [ 3;\infty \right )\)
\(x\in \left [ -3;4\right ] \)
\(x\in \left [ -4;3\right ] \)
\(x\in \left (-\infty ;-4\right )\cup \left (3;\infty \right )\)
\(x\in \left (-\infty ;-3\right ] \cup \left [ 4;\infty \right )\)
9000020405
Level:
A
Identify an equation which does not have the set
\(K = \{ - 3;6\}\) as the
set of all solutions of this equation.
\(3x^{2} - 9x + 54 = 0\)
\(2x^{2} - 6x - 36 = 0\)
\(\frac{1}
{3}x^{2} - x - 6 = 0\)
\(- x^{2} + 3x + 18 = 0\)
9000020407
Level:
A
In the following list identify an equation with real solution.
\(- 0.5x^{2} + 2x + 3 = 0\)
\(- x^{2} + 4x - 5 = 0\)
\(2x^{2} - 3x + 3 = 0\)
\(x^{2} - x + 1 = 0\)
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.
9000022301
Level:
B
Find the solution set of the quadratic inequality.
\[
x^{2} - 8x + 16\leq 0
\]
\(\{4\}\)
\(\emptyset \)
\(\mathbb{R}\setminus \{4\}\)
\(\mathbb{R}\)
\((-\infty ;4)\cup (4;\infty )\)
9000021703
Level:
B
Solve the following inequality.
\[
(x - 2)^{2}\geq (x + 1)(x - 5)
\]
\(x\in \mathbb{R}\)
\(x\in \emptyset \)
\(x\in \left (-\infty ; \frac{9}
{8}\right ] \)
\(x\in \left [ \frac{9}
{8};\infty \right )\)