What are the solutions to the equation z^2-z+2=0 ?

The solutions to the equation z^2-z+2=0 are z= 1/2+i(sqrt(7))/2 ,z= 1/2-i(sqrt(7))/2

Find the zeros of z^2-z+2=0

The zeros of z^2-z+2=0 are z= 1/2+i(sqrt(7))/2 ,z= 1/2-i(sqrt(7))/2

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z^{2} - z + 2 = 0

z = \frac{1}{2} + i \frac{7}{2}, z = \frac{1}{2} - i \frac{7}{2}

Solution steps

z^{2} - z + 2 = 0

Solve with the quadratic formula

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

Simplify

(- 1)^{2} - 4 \cdot 1 \cdot 2 : 7 i

z_{1, 2} = \frac{- ( - 1 ) \pm 7 i}{2 \cdot 1}

Separate the solutions

z_{1} = \frac{- ( - 1 ) + 7 i}{2 \cdot 1}, z_{2} = \frac{- ( - 1 ) - 7 i}{2 \cdot 1}

z = \frac{- ( - 1 ) + 7 i}{2 \cdot 1} : \frac{1}{2} + i \frac{7}{2}

z = \frac{- ( - 1 ) - 7 i}{2 \cdot 1} : \frac{1}{2} - i \frac{7}{2}

The solutions to the quadratic equation are:

z = \frac{1}{2} + i \frac{7}{2}, z = \frac{1}{2} - i \frac{7}{2}

2 x^{2} + 8 x = 54

0 = 3 x^{2} + 16 x + 5

6 - 2 x^{2} = 0

20 x^{2} = - 3 x

x, x^{2} + y^{2} + z^{2} + 8 x - 6 y - 4 z - 7 = 0

What are the solutions to the equation z^2-z+2=0 ?
The solutions to the equation z^2-z+2=0 are z= 1/2+i(sqrt(7))/2 ,z= 1/2-i(sqrt(7))/2
Find the zeros of z^2-z+2=0
The zeros of z^2-z+2=0 are z= 1/2+i(sqrt(7))/2 ,z= 1/2-i(sqrt(7))/2