9000025605
Level:
A
Find the interval which contains all the solutions of the following quadratic
equation.
\[
\text{$5x^{2} - 3x - 2 = 0$}
\]
\((-0.5;2)\)
\([ - 1;0] \)
\([ 0;4)\)
\([ - 3;1)\)
Quadratic equations and inequalities
9000025603
Level:
A
In the following list identify an equation equivalent to the following quadratic
equation.
\[
2(x - 8)\left (x + \frac{1}
{2}\right ) = 0
\]
\(2x^{2} - 15x - 8 = 0\)
\(2x^{2} - 8x + \frac{1}
{2} = 0\)
\(8x^{2} - 15x + \frac{1}
{2} = 0\)
\(8x^{2} - 8x - 1 = 0\)
9000025601
Level:
A
Which of the quadratic equations from the following list has all solutions in the interval
\([ - 5;3] \)?
\(x^{2} - 2x - 3 = 0\)
\(x^{2} - 3x - 10 = 0\)
\(x^{2} - 2x - 15 = 0\)
\(x^{2} - 3x - 18 = 0\)
9000025602
Level:
A
In the following list identify a set which contains at least one solution of the quadratic
equation \(x^{2} - 121 = 0\).
\(\{ - 11;1;13\}\)
\(\{ - 5;0;5;10\}\)
\(\{3;7;9;19\}\)
\(\{ - 15;-12;-7\}\)
9000025604
Level:
A
In the following list identify an equation which does not have solution in the set of
real numbers.
\(8x^{2} - x + 1 = 0\)
\(8x^{2} + 8x - 1 = 0\)
\(8x^{2} - 8x + 1 = 0\)
\(8x^{2} - x - 1 = 0\)
9000025606
Level:
A
In the following list identify a quadratic equation which has a unique solution.
\(x^{2} + 2x + 1 = 0\)
\(x^{2} - 3x - 1 = 0\)
\(x^{2} + 2x - 1 = 0\)
\(x^{2} - 3x + 1 = 0\)
9000022809
Level:
B
Find the solution set of the following quadratic inequality.
\[
4x^{2} + 4x + 1 < 0
\]
\(\emptyset \)
\(\mathbb{R}\)
\(\left \{\frac{1}
{2}\right \}\)
\(\left \{-\frac{1}
{2}\right \}\)
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
\(x = 2\)
\(x\in \mathbb{R}\)