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
\(x = 2\)
\(x\in \mathbb{R}\)
Quadratic equations and inequalities
9000022304
Level:
B
Find all the values of \(x\)
at which the following expression attains nonnegative value.
\[
x^{2} + x - 12
\]
\(x\in \left (-\infty ;-4\right ] \cup \left [ 3;\infty \right )\)
\(x\in \left [ -3;4\right ] \)
\(x\in \left [ -4;3\right ] \)
\(x\in \left (-\infty ;-4\right )\cup \left (3;\infty \right )\)
\(x\in \left (-\infty ;-3\right ] \cup \left [ 4;\infty \right )\)
9000022805
Level:
B
The solution set of one of the following inequalities is the interval
\([ 3;5] \).
Identify this inequality.
\(x^{2} - 8x + 15\leq 0\)
\(x^{2} + 8x + 15\leq 0\)
\(x^{2} - 8x + 15\geq 0\)
\(x^{2} + 8x + 15\geq 0\)
9000022806
Level:
B
For an integer variable \(x\)
find the solution set of the following quadratic inequality.
\[
2x^{2} - x - 6\leq 0
\]
\(\{ - 1;0;1;2\}\)
\(\{ - 2;-1;0;1\}\)
\(\{0;1;2;3\}\)
\(\{ - 3;-2;-1;0\}\)
9000022303
Level:
B
The solution set of one of the following quadratic inequalities is the interval
\((2;5)\).
Determine this inequality.
\(x^{2} - 7x + 10 < 0\)
\(x^{2} + 7x + 10 > 0\)
\(x^{2} - 7x + 10\leq 0\)
\(x^{2} + 7x + 10\geq 0\)
\(x^{2} - 7x + 10 > 0\)
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.
\[
(x - 2)^{2}\geq (x + 1)(x - 5)
\]
\(x\in \mathbb{R}\)
\(x\in \emptyset \)
\(x\in \left (-\infty ; \frac{9}
{8}\right ] \)
\(x\in \left [ \frac{9}
{8};\infty \right )\)
9000021803
Level:
B
Solve the following inequality.
\[
(3x - 1)(2 - 4x) < 0
\]
\(x\in \left (-\infty ; \frac{1}
{3}\right )\cup \left (\frac{1}
{2};\infty \right )\)
\(x\in \left (\frac{1}
{3}; \frac{1}
{2}\right )\)
\(x\in \left (-\infty ; \frac{1}
{2}\right )\)
\(x\in \left (\frac{1}
{3};\infty \right )\)
9000020404
Level:
A
Find a number which is a sum of one half of the bigger solution of
\[
x^{2} - 10x + 24 = 0
\]
and a double of the smaller solution of
\[
-x^{2} + 10x - 16 = 0.
\]
\(7\)
\(12\)
\(6\)
\(14\)
9000020909
Level:
B
The sum of squares of two consecutive integers is
\(1201\).
Identify these integers.
\(24\)
and \(25\)
\(23\)
and \(24\)
\(25\)
and \(26\)
\(26\)
and \(27\)