9000028309
Level:
C
Find the sum of all real solutions of the following equation.
\[
x^{4} + x^{3} + x^{2} + x = 0
\]
\(- 1\)
\(0\)
\(5\)
\(6\)
C
9000031107
Level:
C
Solve the following system of equations and identify a correct statement.
\[\begin{aligned}
\sqrt{x} = y & &
\\x^{2} + y^{2} = 6 & &
\end{aligned}\]
The system has a unique solution.
The system does not have any solution.
The system has two solutions.
The system has more than two solutions.
9000029306
Level:
C
Find the solution set of the following inequality.
\[
x^{3} - 3x^{2} + 3x - 1 < 0
\]
\(\left (-\infty ;1\right )\)
\(\emptyset \)
\(\mathbb{R}\)
\(\left (3;\infty \right )\)
9000031006
Level:
C
The following equation has a double solution
\(x = 1\). Find
all solutions.
\[
x^{4} + 2x^{3} - 3x^{2} - 4x + 4 = 0
\]
\(K = \{ - 2;1\}\)
\(K = \{ - 2;1;2\}\)
\(K = \{ - 2;0;1\}\)
another answer
9000031007
Level:
C
Find the sum of the solutions of the following equation.
\[
x^{3} + 2x^{2} - x - 2 = 0
\]
\(- 2\)
\(3\)
\(- 3\)
\(- 1\)
9000028410
Level:
C
Find the condition which is equivalent to the fact that the equation
\(ax^{2} + bx + c = 0\) with
\(x\in \mathbb{R}\) and real
coefficients \(a\),
\(b\),
\(c\) has
two solutions and one of the solutions is a reciprocal value of the second solution.
\(b^{2} - 4ac > 0\text{ and }\frac{c}
{a} = 1\)
\(b^{2} - 4ac > 0\text{ and }a = c\)
\(b^{2} - 4ac > 0\text{ and }\frac{c}
{a} = -1\)
\(b^{2} - 4ac > 0\text{ and }a = -c\)
9000025807
Level:
C
In the following list identify a true statement on the function
\(f\).
\[
f(x) = \frac{-2(3x + 1)}
{(2x + 3)(2 - x)}
\]
\(f(x) > 0 \iff x\in \left (-\frac{3}
{2};-\frac{1}
{3}\right )\cup (2;\infty )\)
\(f(x) > 0 \iff x\in \left (-\infty ;-\frac{3}
{2}\right )\cup \left (-\frac{1}
{3};2\right )\)
\(f(x) > 0 \iff x\in \left (-\frac{3}
{2};2\right )\)
\(f(x) > 0 \iff x\in \left (-\infty ;-\frac{3}
{2}\right )\cup (2;\infty )\)
9000026001
Level:
C
Which part of the plane describes the solution of the following system of
inequalities?
\[\begin{aligned}
x +\phantom{ 3}y\leq &3 & &
\\y - 2x < & - 1 & &
\end{aligned}\]
blue
red
green
yellow
9000026002
Level:
C
Which part of the plane describes the solution of the following system of
inequalities?
\[\begin{aligned}
x + y > &2 + x & &
\\y + 1\leq &x + 1 & &
\end{aligned}\]
green
red
yellow
blue
9000026003
Level:
C
Which part of the plane describes the solution of the following system of
inequalities?
\[\begin{aligned}
2x - y\geq &2 & &
\\2x + y\geq & - 2 & &
\end{aligned}\]
yellow
red
green
blue