9000028301
Level:
B
The following equation has a solution
\(x = 1\). Find
the sum of the remaining real solutions.
\[
x^{3} - 7x + 6 = 0
\]
\(- 1\)
\(1\)
\(0\)
\(2\)
Higher degree equations and inequalities
9000028306
Level:
A
Find the sum of all real solutions of the following equation.
\[
\left (3 - x\right )\left (x^{2} - 4\right ) = 0
\]
\(3\)
\(0\)
\(2\)
\(5\)
9000025805
Level:
A
In the following list identify a true statement on the function
\(f\).
\[
f(x) = (x + 1)(x + 2)(x - 3)
\]
\(f(x) < 0 \iff x\in (-\infty ;-2)\cup (-1;3)\)
\(f(x) < 0 \iff x\in \left (-\infty ;-\frac{3}
{2}\right )\cup (1;3)\)
\(f(x) < 0 \iff x\in \left (-\infty ;-\frac{3}
{2}\right )\cup (3;\infty )\)
\(f(x) < 0 \iff x\in \left (-\frac{3}
{2};-1\right )\cup (3;\infty )\)
9000019803
Level:
B
Find the solution set of the following equation.
\[
x^{4} - 5x^{2} + 4 = 0
\]
\(\left \{-2;-1;1;2\right \}\)
\(\left \{-1;1\right \}\)
\(\left \{-2;2\right \}\)
\(\left \{1;2\right \}\)
9000019804
Level:
B
Assuming \(x\in \mathbb{R}\), find the solution set of the following equation.
\[
x^{4} - 16 = 0
\]
\(\left \{-2;2\right \}\)
\(\left \{-\sqrt{2};\sqrt{2}\right \}\)
\(\left \{-4;4\right \}\)
\(\left \{-2;-\sqrt{2};\sqrt{2};2\right \}\)
9000019801
Level:
A
Assuming \(x\in \mathbb{N}\),
find the solution set of the following equation.
\[
x^{3} - 6x^{2} + 9x = 0
\]
\(\left \{3\right \}\)
\(\emptyset \)
\(\left \{0;3\right \}\)
\(\left \{-3;3\right \}\)
9000019802
Level:
A
Assuming \(x\in \mathbb{N}\),
find the solution set of the following equation.
\[
2x^{3} - 3x^{2} = 0
\]
\(\emptyset \)
\(\left \{0\right \}\)
\(\left \{2\right \}\)
\(\left \{0; \frac{3}
{2}\right \}\)
9000019805
Level:
B
Assuming \(x\in \mathbb{R}\), find the solution set of the following equation.
\[
x^{4} + 2x^{2} + 1 = 0
\]
\(\emptyset \)
\(\left \{-1;1\right \}\)
\(\left \{-2;2\right \}\)
\(\left \{0\right \}\)
9000019806
Level:
B
Find the smallest integer solution of the following equation.
\[
x^{4} - 2x^{3} - x^{2} + 2x = 0
\]
\(- 1\)
\(0\)
\(1\)
\(2\)
9000019807
Level:
A
Assuming \(x\in \mathbb{R}\), find the solution set of the following equation.
\[
\left (3x + 2\right )\left (x\sqrt{2} + 1\right )\left (x^{2} + 1\right ) = 0
\]
\(\left \{-\frac{\sqrt{2}}
{2} ;-\frac{2}
{3}\right \}\)
\(\left \{-\frac{2}
{3}; \frac{1}
{\sqrt{2}}\right \}\)
\(\left \{\frac{2}
{3}; \frac{1}
{\sqrt{2}}\right \}\)
\(\left \{-1;-\frac{\sqrt{2}}
{2} ;-\frac{2}
{3}\right \}\)