9000031007
Level:
C
Find the sum of the solutions of the following equation.
\[
x^{3} + 2x^{2} - x - 2 = 0
\]
\(- 2\)
\(3\)
\(- 3\)
\(- 1\)
C
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.
\(b^{2} - 4ac > 0\text{ and }\frac{c}
{a} = 1\)
\(b^{2} - 4ac > 0\text{ and }a = c\)
\(b^{2} - 4ac > 0\text{ and }\frac{c}
{a} = -1\)
\(b^{2} - 4ac > 0\text{ and }a = -c\)
9000028409
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 \(a\),
\(b\),
\(c\) does
not have a real solution.
\((b^{2} - 4ac < 0\text{ and }a\not = 0)\text{ or }(a = b = 0\text{ and }c\not = 0)\)
\(b^{2} - 4ac < 0\)
\(b^{2} - 4ac < 0\text{ and }a\not = 0\)
\((b^{2} - 4ac < 0\text{ and }a\not = 0)\text{ or }(ab = 0\text{ and }c\not = 0)\)
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
9000026004
Level:
C
Which part of the plane describes the solution of the following system of
inequalities?
\[\begin{aligned}
2y - x\geq &4 & &
\\2y - x\geq & - 2 & &
\end{aligned}\]
blue
red
yellow
9000026005
Level:
C
Which part of the plane describes the solution of the following system of
inequalities?
\[\begin{aligned}
x\leq &3 & &
\\5x > &9 - 3y & &
\end{aligned}\]
yellow
red
green
blue
9000026006
Level:
C
In the picture, the shaded region corresponds to the set of points that is the solution to one of the given systems of inequalities. Which of the systems is it?
\(\begin{aligned}x +\phantom{ 2}y&\geq 3 &
\\y - 2x& < -1
\\ \end{aligned}\)
\(\begin{aligned}x +\phantom{ 2}y& > 3 &
\\y - 2x& < -1
\\ \end{aligned}\)
\(\begin{aligned}x +\phantom{ 2}y&\leq 3 &
\\y - 2x& < -1
\\ \end{aligned}\)
\(\begin{aligned}x +\phantom{ 2}y& < 3 &
\\y - 2x& > -1
\\ \end{aligned}\)
9000026007
Level:
C
In the picture, the shaded region corresponds to the set of points that is the solution to one of the given systems of inequalities. Which of the systems is it?
\(\begin{aligned}y & < 2 &
\\y + 1&\geq x + 1
\\ \end{aligned}\)
\(\begin{aligned}y &\geq 2 &
\\y + 1& < x + 1
\\ \end{aligned}\)
\(\begin{aligned}y & > 2 &
\\y + 1&\leq x + 1
\\ \end{aligned}\)
\(\begin{aligned}y&\leq 2 &
\\y& > x
\\ \end{aligned}\)