Quadratic equations with complex roots

2010013201

Level:

Find the complex roots of the following quadratic equation.

3 x^{2} + 8 = 0

x_{1} = - \frac{2 \sqrt{6}}{3} i, x_{2} = \frac{2 \sqrt{6}}{3} i

x_{1} = - \frac{\sqrt{6}}{3} i, x_{2} = \frac{\sqrt{6}}{3} i

x_{1} = - \frac{\sqrt{12}}{3} i, x_{2} = \frac{\sqrt{12}}{3} i

x_{1} = - \frac{\sqrt{6}}{6} i, x_{2} = \frac{\sqrt{6}}{6} i

Level:

Find the solution set of the following equation.

4 x^{2} + 9 = 0

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

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

{- \frac{9}{4} i; \frac{9}{4} i}

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

Level:

Find the sum of the reciprocal values of the solutions of

5 x^{2} - 2 x + 1 = 0

2

\frac{2}{5}

\frac{2}{5} + \frac{4}{5} i

- \frac{2}{5}

Level:

Find the factorization of the following quadratic polynomial in the set of polynomial with complex valued coefficients.

2 x^{2} + 32

2 (x + 4 i) (x - 4 i)

2 (x - 4 i)^{2}

(x + 4 i) (x - 4 i)

2 (x + 4 i)^{2}

Level:

Find the factorization of the following quadratic polynomial in the set of polynomial with complex valued coefficients.

2 x^{2} + 4 x + 5

2 (x + 1 + \frac{\sqrt{6}}{2} i) (x + 1 - \frac{\sqrt{6}}{2} i)

2 (x - 1 + \frac{\sqrt{6}}{2} i) (x - 1 - \frac{\sqrt{6}}{2} i)

(x + 1 - \frac{\sqrt{6}}{2} i) (x + 1 + \frac{\sqrt{6}}{2} i)

(x - 1 - \frac{\sqrt{6}}{2} i) (x - 1 + \frac{\sqrt{6}}{2} i)

Level:

Solve the following quadratic equation in the complex plane.

4 x^{2} + 12 = 0

x_{1, 2} = \pm i \sqrt{3}

x_{1, 2} = \pm 3

x_{1, 2} = \pm 3 i

x_{1, 2} = \pm \sqrt{3}

Level:

Solve the following quadratic equation in the complex plane.

2 x^{2} + x + 1 = 0

x_{1, 2} = \frac{- 1 \pm i \sqrt{7}}{4}

x_{1, 2} = \frac{- 1 \pm i \sqrt{7}}{2}

x_{1, 2} = \frac{1 \pm i \sqrt{7}}{4}

x_{1, 2} = \frac{1 \pm i \sqrt{7}}{2}

Level:

Solve the following quadratic equation in the complex plane.

x^{2} + 4 x + 5 = 0

x_{1} = - 2 + i

x_{2} = - 2 - i

x = - 2

x_{1} = 2 + i

x_{2} = 2 - i

x_{1} = - 3

x_{2} = - 1

Level:

Solve the following quadratic equation in the complex plane.

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

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

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

x_{1} = - \frac{1}{3}

x_{1} = \frac{1}{3} + \frac{\sqrt{5}}{3}

x_{2} = \frac{1}{3} + \frac{\sqrt{5}}{3}

x_{1} = \frac{1}{3} + \frac{\sqrt{5}}{3} i

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

Level:

Find the factorization of the quadratic polynomial

x^{2} + 2 x + 2

in the set of polynomials with complex valued coefficients.

(x + 1 + i) (x + 1 - i)

(x - 1 + i) (x - 1 - i)

(x - i) (x + i)

(x - 1 + i) (x + 1 - i)