9000028304
Level:
C
The following equation has solutions
\(x_1= 1\) and
\(x_2 = 3\). Find
the sum of the remaining real solutions.
\[
x^{4} - 12x^{3} + 47x^{2} - 72x + 36 = 0
\]
\(8\)
\(- 1\)
\(3\)
\(5\)
C
9000028305
Level:
C
The following equation has solution
\(x_1= 2\) and
\(x_2= 4\). Find
the sum of the remaining real solutions.
\[
x^{4} - 6x^{3} - x^{2} + 54x - 72 = 0
\]
\(0\)
\(- 1\)
\(1\)
\(2\)
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
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?
\(\begin{aligned}x +\phantom{ 2}y&\geq 3 &
\\y - 2x& < -1
\\ \end{aligned}\)
\(\begin{aligned}x +\phantom{ 2}y& > 3 &
\\y - 2x& < -1
\\ \end{aligned}\)
\(\begin{aligned}x +\phantom{ 2}y&\leq 3 &
\\y - 2x& < -1
\\ \end{aligned}\)
\(\begin{aligned}x +\phantom{ 2}y& < 3 &
\\y - 2x& > -1
\\ \end{aligned}\)
9000025803
Level:
C
Find all intersections of the graph of the following function with
\(x\)-axis.
\[
f(x) = \frac{2x + 1}
{x^{2} - x - 6}
\]
\(X = \left [-\frac{1}
{2};0\right ]\)
\(X = \left [-\frac{1}
{6};0\right ]\)
\(X_{1} = [-2;0]\),
\(X_{2} = [3;0]\)
\(X_{1} = [-2;0]\),
\(X_{2} = \left [-\frac{1}
{2};0\right ]\),
\(X_{3} = [3;0]\)