2000001507
Level:
B
Find the quadratic equation with real valued coefficients and one of the solutions \(\frac{1}{4}i\).
\( 16x^2 +1 =0\)
\( 16x^2 -1 =0\)
\( x^2 -\frac{1}{4} =0\)
\( x^2 +\frac{1}{4} =0\)
B
2000001505
Level:
B
Which of the numbers below does not satisfy the equation \(2x^2=-16\)?
\( \sqrt{8}(\cos{\pi} +i\sin{\pi})\)
\( 2\sqrt{2}(\cos{\frac{\pi}{2}} +i\sin{\frac{\pi}{2}})\)
\( 2\sqrt{2}\left(\cos{\left(-\frac{\pi}{2}\right)} +i\sin{\left(-\frac{\pi}{2}\right)}\right)\)
\( 2\sqrt{2}i\)
2000001205
Level:
B
Find all \(x \in \mathbb{R}\) such that the given relation is true.
\[ -|x|=|-x|\]
\( x \in \{0\}\)
\( x \in [ 0; \infty) \)
\( x \in (-\infty;0] \)
\(x \in \mathbb{R} \)
No such \(x\) exists.
2000001204
Level:
B
Find all \(x \in \mathbb{R}\) such that the given relation is true.
\[- |x|=-x\]
\( x \in [ 0; \infty) \)
\( x \in (-\infty;0] \)
\(x \in \mathbb{R} \)
No such \(x\) exists.
\( x \in \{0\}\)
2000001203
Level:
B
Find all \(x \in \mathbb{R}\) such that the given relation is true.
\[ |-x|=-x\]
\( x \in (-\infty;0] \)
\( x \in [ 0; \infty) \)
\(x \in \mathbb{R} \)
No such \(x\) exists.
\( x \in \{0\}\)
2000001202
Level:
B
Find all \(x \in \mathbb{R}\) such that the given relation is true.
\[ |x|=-x\]
\( x \in (-\infty;0] \)
\( x \in [ 0; \infty) \)
\(x \in \mathbb{R} \)
No such \(x\) exists.
\( x \in \{0\}\)
2000001201
Level:
B
Find all \(x \in \mathbb{R}\) such that the given relation is true.
\[ |x|=x\]
\( x \in [ 0;\infty) \)
\( x \in (-\infty;0] \)
\( x \in\mathbb{R}\)
No such \(x\) exists.
\( x \in \{0\} \)
2000000705
Level:
B
Use the given graph of the function \(f: y=(x-2)(x-3)=x^2-5x+6\) to solve the inequality \((x-2)(x-3)< 0\).
\(x \in (2;3)\)
\(x \in \mathbb{R}\setminus \{2;3\}\)
\(x \in (-\infty;2)\cup(3;\infty)\)
\(x \in \emptyset\)
2000000704
Level:
B
Use the given graph of the function \(f: y=-x^2+5x\) to solve the inequality \(-x^2+5x< 0\).
\(x \in (-\infty;0)\cup(5;\infty)\)
\(x \in \mathbb{R}\setminus \{0;5\}\)
\(x \in(0;5)\)
\(x \in (0;6.25)\)
2000000703
Level:
B
Use the given graph of the function \(f: y=x^2-4\) to solve the inequality \(x^2-4< 0\).
\(x \in (-2;2)\)
\(x \in \mathbb{R}\setminus \{-2;2\}\)
\(x \in (-4;0)\)
\(x \in (-\infty;-2) \cup (2;\infty)\)