1003028801
Level:
A
For the next equation, find the sum of all the roots from the set of natural numbers. Multiple roots, if any, count only once.
\[ \left(x^2+4\right)\left(x^2-9\right)=0 \]
\( 3 \)
\( -5 \)
\( 5 \)
\( -1 \)
Higher degree equations and inequalities
1003028802
Level:
A
Find the sum of all the real roots of the next equation. Multiple roots, if any, count only once.
\[ \left(x^2+9\right)\left(x^2-1\right)\left(x+1\right)=0 \]
\( 0 \)
\( 1 \)
\( -1 \)
\( 3 \)
1003028803
Level:
A
Find all the real roots of the equation.
\[ \left(x^2+1\right)\left(x^2-2\right)\left(x+2\right)=0 \]
\( \left\{-2;-\sqrt2;\sqrt2\right\} \)
\( \left\{-2;-\sqrt2;-1;1;\sqrt2\right\} \)
\( \left\{-2;-1;1;2\right\} \)
\( \left\{-2;-\sqrt2;-1;\sqrt2\right\} \)
1003028804
Level:
A
For the next equation, find the sum of all the roots from the set of natural numbers. Multiple roots, if any, count only once.
\[ \left(x^3+1\right)\left(x^2-4\right)=0 \]
\( 2 \)
\( -1 \)
\( 3 \)
\( 1 \)
1003028805
Level:
A
Find the sum of all the real roots of the next equation. Multiple roots, if any, count only once.
\[ \left(x^3+8\right)\left(x^2-1\right)\left(x+1\right)=0 \]
\( -2 \)
\( 0 \)
\( 2 \)
\( -3 \)
1003028806
Level:
A
Find all the real roots of the equation.
\[ \left(x^4-1\right)\left(x^3-8\right)\left(x^2-2\right)=0 \]
\( \left\{-\sqrt2;-1;1;\sqrt2;2\right\} \)
\( \left\{-2;-1;1;2\right\} \)
\( \left\{-\sqrt2;-1;1;\sqrt2\right\} \)
\( \left\{-\sqrt2;\sqrt2;2\right\} \)
1003028901
Level:
A
Find the factored form of the equation.
\[ x^4-16=0 \]
\( \left(x^2+4\right)\left(x-2\right)\left(x+2\right)=0 \)
\( \left(x-2\right)^2\left(x+2\right)^2=0 \)
\( \left(x-2\right)^4=0 \)
\( \left(x+4\right)\left(x-2\right)\left(x+2\right)=0 \)
1003028902
Level:
A
Find the factored form of the equation.
\[ x^4+2x^2+x^3+2x=0 \]
\( x\left(x^2+2\right)\left(x+1\right)=0 \)
\( x\left(x^2+1\right)\left(x+1\right)=0 \)
\( x\left(x^2+1\right)\left(x+2\right)=0 \)
\( x\left(x^2+2\right)\left(x+2\right)=0 \)
1003028903
Level:
A
Find the factored form of the equation.
\[ x^3-2x^2-x+2=0 \]
\( (x-2)(x-1)(x+1)=0 \)
\( x(x-1)(x-2)=0 \)
\( x^2(x-2)=0 \)
\( x(x+1)(x-2)=0 \)
1003028904
Level:
A
Find the factored form of the equation.
\[ x^4+2x^2=0 \]
\( x^2\left(x^2+2\right)=0 \)
\( \left(x^2-2\right)\left(x^2+2\right)=0 \)
\( \left(x^2+\sqrt2x\right)\left(x^2-\sqrt2x\right)=0 \)
\( \left(x^2+\sqrt2x\right)\left(x^2+\sqrt2x\right)=0 \)