What are the solutions to the equation z^2+1/2 z+1/4 =0 ?

The solutions to the equation z^2+1/2 z+1/4 =0 are z=-1/4+i(sqrt(3))/4 ,z=-1/4-i(sqrt(3))/4

Find the zeros of z^2+1/2 z+1/4 =0

The zeros of z^2+1/2 z+1/4 =0 are z=-1/4+i(sqrt(3))/4 ,z=-1/4-i(sqrt(3))/4

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

z^{2} + \frac{1}{2} z + \frac{1}{4} = 0

z = - \frac{1}{4} + i \frac{3}{4}, z = - \frac{1}{4} - i \frac{3}{4}

Solution steps

z^{2} + \frac{1}{2} z + \frac{1}{4} = 0

Find Least Common Multiplier of

2, 4 : 4

Multiply by LCM=

4

z^{2} \cdot 4 + \frac{1}{2} z \cdot 4 + \frac{1}{4} \cdot 4 = 0 \cdot 4

Simplify

4 z^{2} + 2 z + 1 = 0

Solve with the quadratic formula

z_{1, 2} = \frac{- 2 \pm 2 ^{2} - 4 \cdot 4 \cdot 1}{2 \cdot 4}

Simplify

2^{2} - 4 \cdot 4 \cdot 1 : 23 i

z_{1, 2} = \frac{- 2 \pm 2 3 i}{2 \cdot 4}

Separate the solutions

z_{1} = \frac{- 2 + 2 3 i}{2 \cdot 4}, z_{2} = \frac{- 2 - 2 3 i}{2 \cdot 4}

z = \frac{- 2 + 2 3 i}{2 \cdot 4} : - \frac{1}{4} + i \frac{3}{4}

z = \frac{- 2 - 2 3 i}{2 \cdot 4} : - \frac{1}{4} - i \frac{3}{4}

The solutions to the quadratic equation are:

z = - \frac{1}{4} + i \frac{3}{4}, z = - \frac{1}{4} - i \frac{3}{4}

4 [5 - 8 (4 c - 3)] = 12 (1 - 13 c) - 8

lo g_{4} (4) + lo g_{4} (16)

6 x = 5

- 3 w - 3 x - 7 w + 4 x - 2 w

x^{2} - 4 y^{2} - 6 x + 9

What are the solutions to the equation z^2+1/2 z+1/4 =0 ?
The solutions to the equation z^2+1/2 z+1/4 =0 are z=-1/4+i(sqrt(3))/4 ,z=-1/4-i(sqrt(3))/4
Find the zeros of z^2+1/2 z+1/4 =0
The zeros of z^2+1/2 z+1/4 =0 are z=-1/4+i(sqrt(3))/4 ,z=-1/4-i(sqrt(3))/4