2000001504
Level:
A
Find the product of the complex roots of the equation \(x^2 = -25\).
\( 25 \)
\( -25i\)
\( -25\)
\( 25i\)
Quadratic equations with complex roots
2000001503
Level:
A
Find the sum of the complex roots of the equation \(3x^2 +27=0\).
\( 0\)
\( 6\)
\( -6i\)
\( 6i\)
2000001502
Level:
A
Find the complex roots of the equation \(2x^2=-8\).
\( x_1 = 2i;~x_2=-2i\)
\( x_1 = x_2=2i\)
\( x_1 =x_2=-2i\)
The equation has no solution.
2000001501
Level:
A
Solve the quadratic equation \( x^2 +1 =0\) in the set of complex numbers.
\( x_{1,2} = \pm i\)
\( x_{1,2} = i\)
\( x_{1,2} = -i\)
\( x_{1,2} = \pm 1\)
Quadratic Equations with Complex Coefficients
Submitted by ladislav.foltyn on Fri, 05/24/2019 - 15:311003107511
Level:
C
Find the solution set of the following quadratic equation in the complex plane.
\[ 2x^2-x=3\mathrm{i}x+2 \]
\( \left\{-\frac12+\frac12\mathrm{i}; 1+\mathrm{i} \right\} \)
\( \left\{-\frac12+\mathrm{i}; 1+\frac12\mathrm{i} \right\} \)
\( \left\{\frac12-\frac12\mathrm{i}; -1-\mathrm{i} \right\} \)
\( \left\{\frac12-\mathrm{i}; -1-\frac12\mathrm{i} \right\} \)
\( \left\{-\frac12-\frac12\mathrm{i}; 1-\mathrm{i} \right\} \)
\( \left\{\frac12+\mathrm{i}; -1+\frac12\mathrm{i} \right\} \)
1003107510
Level:
C
Find the solution set of the following quadratic equation in the complex plane.
\[ x+\frac{\mathrm{i}}2=\frac1x+\frac2{\mathrm{i}} \]
\( \left\{-\frac12\mathrm{i};-2\mathrm{i} \right\} \)
\( \left\{\frac12\mathrm{i};2\mathrm{i} \right\} \)
\( \left\{\frac12\mathrm{i};-2\mathrm{i} \right\} \)
\( \left\{-\frac12\mathrm{i};2\mathrm{i} \right\} \)
\( \emptyset \)
1003107509
Level:
C
Find the solution set of the following quadratic equation in the complex plane.
\[ (3-2\mathrm{i})x^2-(2-4\mathrm{i})x + 2 = 0 \]
\( \left\{ 1-\mathrm{i}; \frac1{13}+\frac5{13}\mathrm{i} \right\} \)
\( \left\{ -1+\mathrm{i}; -\frac1{13}-\frac5{13}\mathrm{i} \right\} \)
\( \emptyset \)
\( \left\{ -1+\mathrm{i}; \frac1{13}+\frac5{13}\mathrm{i} \right\} \)
\( \left\{ 1-\mathrm{i}; -\frac1{13}-\frac5{13}\mathrm{i} \right\} \)
1003107508
Level:
C
Find the complex roots of the following quadratic equation.
\[ x^2 + (2 + 2\mathrm{i})x + 2\mathrm{i} = 0 \]
\( x_{1,2}=-1-\mathrm{i} \)
\( x_{1,2}=1+\mathrm{i} \)
\( x_1=1+\mathrm{i}\text{, }\ x_2=-1-\mathrm{i} \)
\( x_1=1-\mathrm{i}\text{, }\ x_2=-1+\mathrm{i} \)
1003107507
Level:
C
Find the solution set of the following quadratic equation in the complex plane.
\[ x^2 +3\mathrm{i}x + 10 = 0 \]
\( \{-5\mathrm{i}; 2\mathrm{i}\} \)
\( \{-2\mathrm{i}; 5\mathrm{i}\} \)
\( \{2-5\mathrm{i}; 5-2\mathrm{i}\} \)
\( \{-2+5\mathrm{i}; -5+2\mathrm{i}\} \)
\( \emptyset \)