9000020003
Level:
A
Find the domain of the following equation.
\[
\sqrt{3x + 6} + \sqrt{8 - 2x} = 11
\]
\([ - 2,4] \)
\((-\infty ,-2] \)
\([ - 2,\infty )\)
\([ 4,\infty )\)
A
9000020401
Level:
A
Solve the following quadratic equation.
\[
-x^{2} + 12x - 20 = 0
\]
\(x_{1} = 2\),
\(x_{2} = 10\)
\(x_{1} = -2\),
\(x_{2} = 10\)
\(x_{1} = -2\),
\(x_{2} = -10\)
\(x_{1} = 2\),
\(x_{2} = -10\)
9000020004
Level:
A
Find the domain of the following equation.
\[
\sqrt{x - 7} + \sqrt{3x + 12} = 5
\]
\([ 7,\infty )\)
\([ - 4,7] \)
\([ - 4,\infty )\)
\((-4,7)\)
9000020402
Level:
A
Identify an equation which does not have real solution.
\(x^{2} - 2x + 5 = 0\)
\(x^{2} - 5 = 0\)
\(x^{2} + 0.8x = 0\)
\(- x^{2} + 2x + 35 = 0\)
9000021706
Level:
A
Find all the values of the parameter \(k\) so that the solution of the following equation is bigger than \(10\).
\[
3x - 18 = \frac{10x - 4k}
{2}
\]
\(k\in (19,\infty )\)
\(k\in \{9\}\)
\(k\in (-\infty ,1)\)
\(k\in (9,\infty )\)
9000020407
Level:
A
In the following list identify an equation with real solution.
\(- 0.5x^{2} + 2x + 3 = 0\)
\(- x^{2} + 4x - 5 = 0\)
\(2x^{2} - 3x + 3 = 0\)
\(x^{2} - x + 1 = 0\)
9000021707
Level:
A
Find all the values of the parameter \(k\) so that the solution of the following equation is positive.
\[
2kx + k = 4x + 3
\]
\(k\in (2,3)\)
\(k > 0\)
\(k\in (3,\infty )\)
\(k\in (-\infty ,3)\)
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.
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
\[
-x^{2} + 10x - 16 = 0.
\]
\(7\)
\(12\)
\(6\)
\(14\)
9000020006
Level:
A
Identify a true statement referring to the solution of the following equation.
\[
\sqrt{3x - 8} = x - 6
\]
The equation has a unique solution and this solution is an odd number.
The equation has two solutions, the sum of these solutions is divisible by
\(5\).
The equation has a unique solution and this solution is an even number.
The equation does not have a solution in
\(\mathbb{R}\).