Higher degree equations and inequalities
Polynomial Inequalities
Submitted by michaela.bailova on Fri, 04/05/2024 - 12:572010009707
Level:
A
Find the factored form of the equation.
\[ x^4-81=0 \]
\( \left(x^2+9\right)\left(x-3\right)\left(x+3\right)=0 \)
\( \left(x-3\right)^2\left(x+3\right)^2=0 \)
\( \left(x-3\right)^4=0 \)
\( \left(x+9\right)\left(x-3\right)\left(x+3\right)=0 \)
2010009706
Level:
A
Find the sum of all the natural roots of the next equation. Multiple roots, if any, count only once.
\[ \left(x^3+8\right)\left(x^2-1\right)=0 \]
\( 1\)
\( -1\)
\( 3\)
\( 0\)
2010009705
Level:
A
Find the sum of all the natural roots of the next equation. Multiple roots, if any, count only once.
\[ \left(x^2+1\right)\left(x^2-16 \right)=0 \]
\( 4\)
\( 3\)
\( 5\)
\( 0\)
2010009704
Level:
A
Find the sum of all real solutions of the following equation.
\[
\left (2 - x\right )\left (x^{2} - 9\right ) = 0
\]
\( 2\)
\( 0\)
\( 5\)
\( 3\)
2010009703
Level:
A
In the following list identify a true statement on the function
\(f\).
\[
f(x) = (x + 3)(x -1)(x - 2)
\]
\(f(x) > 0 \iff x\in (-3;1)\cup (2;\infty)\)
\(f(x) > 0 \iff x\in (-2;-1)\cup (3;\infty)\)
\(f(x) > 0 \iff x\in (-\infty ;-3)\cup (1;2)\)
\(f(x) < 0 \iff x\in (-3;1)\cup (2;\infty)\)