9000028303
Level:
B
The following equation has a solution
\(x = -2\). Find
the sum of the remaining real solutions.
\[
x^{3} + 3x^{2} - 18x - 40 = 0
\]
\(- 1\)
\(1\)
\(0\)
\(4\)
Higher Degree Equations and Inequalities
9000028304
Level:
C
The following equation has solutions
\(x_1= 1\) and
\(x_2 = 3\). Find
the sum of the remaining real solutions.
\[
x^{4} - 12x^{3} + 47x^{2} - 72x + 36 = 0
\]
\(8\)
\(- 1\)
\(3\)
\(5\)
9000025805
Level:
A
In the following list identify a true statement on the function
\(f\).
\[
f(x) = (x + 1)(x + 2)(x - 3)
\]
\(f(x) < 0 \iff x\in (-\infty ,-2)\cup (-1,3)\)
\(f(x) < 0 \iff x\in \left (-\infty ,-\frac{3}
{2}\right )\cup (1,3)\)
\(f(x) < 0 \iff x\in \left (-\infty ,-\frac{3}
{2}\right )\cup (3,\infty )\)
\(f(x) < 0 \iff x\in \left (-\frac{3}
{2},-1\right )\cup (3,\infty )\)
9000019806
Level:
B
Find the smallest integer solution of the following equation.
\[
x^{4} - 2x^{3} - x^{2} + 2x = 0
\]
\(- 1\)
\(0\)
\(1\)
\(2\)
9000019809
Level:
B
Find the factorization of the following equation.
\[
x^{3} + 3x^{2} - x - 3 = 0
\]
\(\left (x + 3\right )\left (x + 1\right )\left (x - 1\right ) = 0\)
\(\left (x - 3\right )\left (x + 1\right )\left (x - 1\right ) = 0\)
\(\left (x + 3\right )\left (x - 3\right )\left (x - 1\right ) = 0\)
\(\left (x + 3\right )\left (x - 3\right )\left (x + 1\right ) = 0\)
9000019810
Level:
B
Find the factorization of the following equation.
\[
5x^{4} - 30x^{2} + 40 = 0
\]
\(5\left (x -\sqrt{2}\right )\left (x + \sqrt{2}\right )\left (x - 2\right )\left (x + 2\right ) = 0\)
\(\left (x -\sqrt{2}\right )\left (x + \sqrt{2}\right )\left (x - 2\right )\left (x + 2\right ) = 0\)
\(5x\left (x -\sqrt{2}\right )\left (x + \sqrt{2}\right )\left (x - 2\right ) = 0\)
\(5x\left (x -\sqrt{2}\right )\left (x + \sqrt{2}\right )\left (x + 2\right ) = 0\)
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.
\[
2x^{3} - 3x^{2} = 0
\]
\(\emptyset \)
\(\left \{0\right \}\)
\(\left \{2\right \}\)
\(\left \{0, \frac{3}
{2}\right \}\)
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.
\[
x^{4} - 16 = 0
\]
\(\left \{-2,2\right \}\)
\(\left \{-\sqrt{2},\sqrt{2}\right \}\)
\(\left \{-4,4\right \}\)
\(\left \{-2,-\sqrt{2},\sqrt{2},2\right \}\)