Quadratic equations with complex roots

1003102501

Level:

Find the set of all complex roots of the following quadratic equation.

9 x^{2} + 2 = 0

{- \frac{\sqrt{2}}{3} i; \frac{\sqrt{2}}{3} i}

{- \sqrt{\frac{2}{3}} i; \sqrt{\frac{2}{3}} i}

{- \frac{2}{3} i; \frac{2}{3} i}

{- \frac{2}{9} i; \frac{2}{9} i}

\emptyset

1003102502

Level:

Find the complex roots of the following quadratic equation.

4 x^{2} + 0.0025 = 0

x_{1} = - \frac{1}{40} i, x_{2} = \frac{1}{40} i

x_{1} = - \frac{1}{4} i, x_{2} = \frac{1}{4} i

x_{1} = - \frac{5}{16} i, x_{2} = \frac{5}{16} i

x_{1} = - \frac{5}{4} i, x_{2} = \frac{5}{4} i

1003102503

Level:

Find the complex roots of the following quadratic equation.

5 x^{2} + 12 = 0

x_{1} = - \frac{2 \sqrt{15}}{5} i, x_{2} = \frac{2 \sqrt{15}}{5} i

x_{1} = - \frac{\sqrt{15}}{5} i, x_{2} = \frac{\sqrt{15}}{5} i

x_{1} = - \frac{\sqrt{12}}{5} i, x_{2} = \frac{\sqrt{12}}{5} i

x_{1} = - \frac{2 \sqrt{3}}{5} i, x_{2} = \frac{2 \sqrt{3}}{5} i

2000001501

Level:

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

2000001502

Level:

Find the complex roots of the equation

2 x^{2} = - 8

x_{1} = 2 i; x_{2} = - 2 i

x_{1} = x_{2} = 2 i

x_{1} = x_{2} = - 2 i

The equation has no solution.

2000001503

Level:

Find the sum of the complex roots of the equation

3 x^{2} + 27 = 0

0

6

- 6 i

6 i

2000001504

Level:

Find the product of the complex roots of the equation

x^{2} = - 25

25

- 25 i

- 25

25 i

2000001506

Level:

Factorize the equation

4 x^{2} + 25 = 0

in the set of complex numbers.

4 (x - \frac{5}{2} i) (x + \frac{5}{2} i) = 0

(2 x + 5) (2 x + 5) = 0

4 (x + \frac{5}{2} i) (x + \frac{5}{2} i) = 0

4 (x - \frac{5}{2} i) (x - \frac{5}{2} i) = 0

2000001509

Level:

Find the right formula for solving the equation

2 x^{2} + 5 x + 5 = 0

x_{1, 2} = \frac{- 5 \pm i \sqrt{15}}{4}

x_{1, 2} = \frac{5 \pm i \sqrt{15}}{4}

x_{1, 2} = \frac{- 5 \pm i \sqrt{15}}{2}

x_{1, 2} = \frac{- 5 i \pm i \sqrt{40}}{4}

2000001512

Level:

Let

x_{1} = 2 - \frac{\sqrt{5}}{2} i

be one of the roots of a quadratic equation with real coefficients. Find the other root

x_{2}

of this equation.

x_{2} = 2 + \frac{\sqrt{5}}{2} i

x_{2} = - 2 - \frac{\sqrt{5}}{2} i

x_{2} = - 2 + \frac{\sqrt{5}}{2} i

x_{2} = \frac{1}{2 - \frac{\sqrt{5}}{2} i}

Quadratic equations with complex roots

1003102501

1003102502

1003102503

2000001501

2000001502

2000001503

2000001504

2000001506

2000001509

2000001512

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