1003028905
Level:
A
Find the factored form of the equation.
\[ x^4+2x^3-3x-6=0 \]
\( \left(x^3-3\right)(x+2) = 0 \)
\( \left(x^3+3\right)(x-2) = 0 \)
\( \left(x^3-2\right)(x+3) = 0 \)
\( \left(x^3+2\right)(x-3) = 0 \)
Higher degree equations and inequalities
1003189104
Level:
A
One of the solutions of the following equation equals \( 1 \). Find the sum of all the remaining solutions.
\[ x^4- x^3+ x - 1=0 \]
\( -1 \)
\( 1 \)
\( 0 \)
\( 2 \)
1003189105
Level:
A
One of the roots of the following equation equals \( 2 \). Find the product of all the remaining roots.
\[ x^5- 2 x^4- 9 x + 18=0 \]
\( -3 \)
\( -1 \)
\( 1 \)
\( 3 \)
1003189106
Level:
A
Given \( x\in\mathbb{R} \), find the solution set of the following equation.
\[ 2x^4+x^3+2x^2+x=0 \]
Hint: Decompose the polynomial on the left side of the equation into factors.
\( \left\{-\frac12;0\right\} \)
\( \{-1;0\} \)
\( \left\{-1;0;\frac12;1\right\} \)
\( \left\{-\frac{\sqrt2}2;0;1;\frac{\sqrt2}2\right\} \)
1003189107
Level:
A
Given \( x\in\mathbb{R} \), find the solution set of the following equation.
\[ -x^4+x^3-x^2+x=0 \]
Hint: Decompose the polynomial on the left side of the equation into factors.
\( \{ 0;1 \} \)
\( \{-1;0\} \)
\( \{-1;0;1\} \)
\( \{-1;1\} \)
1003189108
Level:
A
Find the product of all the real roots of the following equation.
\[ 5x^5-3x^3-5x^2+3=0 \]
\( -\frac35 \)
\( \frac53 \)
\( 0 \)
\( 1 \)
1003189109
Level:
A
Find the sum of all the positive roots of the following equation.
\[ 16x^5-9x^3-16x^2+9=0 \]
\( \frac74 \)
\( 1 \)
\( \frac34 \)
\( 0 \)
2000003801
Level:
A
Assuming \(x\in \mathbb{R}\), find the solution set of the following equation.
\[
x^2(x-1)=0
\]
\( \{0;1\}\)
\( \{-1;0\}\)
\( \{-1;1\}\)
\( \{-1;0;1\}\)
2000003802
Level:
A
Assuming \(x\in \mathbb{R}\), find the solution set of the following equation.
\[
(x^2-1)x=0
\]
\( \{-1;0;1\}\)
\( \{0;1\}\)
\( \{-1;0\}\)
\( \{-1;1\}\)
2000003803
Level:
A
Assuming \(x\in \mathbb{R}\), find the solution set of the following equation.
\[
(x^2+1)(x^2-4)=0
\]
\( \{-2;2\}\)
\( \{-2;-1;1;2\}\)
\( \{-2;-1;2\}\)
\( \{-1;2\}\)