What are the solutions to the equation 4z+z^2+12=0 ?

The solutions to the equation 4z+z^2+12=0 are z=-2+2sqrt(2)i,z=-2-2sqrt(2)i

Find the zeros of 4z+z^2+12=0

The zeros of 4z+z^2+12=0 are z=-2+2sqrt(2)i,z=-2-2sqrt(2)i

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4 z + z^{2} + 12 = 0

z = - 2 + 22 i, z = - 2 - 22 i

Solution steps

4 z + z^{2} + 12 = 0

Write in the standard form

a x^{2} + b x + c = 0

z^{2} + 4 z + 12 = 0

Solve with the quadratic formula

z_{1, 2} = \frac{- 4 \pm 4 ^{2} - 4 \cdot 1 \cdot 12}{2 \cdot 1}

Simplify

4^{2} - 4 \cdot 1 \cdot 12 : 42 i

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

Separate the solutions

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

z = \frac{- 4 + 4 2 i}{2 \cdot 1} : - 2 + 22 i

z = \frac{- 4 - 4 2 i}{2 \cdot 1} : - 2 - 22 i

The solutions to the quadratic equation are:

z = - 2 + 22 i, z = - 2 - 22 i

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

(3 x + 4)^{2} = 24 x + 16

3 x^{2} + x = 1

3 x^{2} - 7 x - 13 = 0

5 x^{2} - 2 x + 12 = 0

What are the solutions to the equation 4z+z^2+12=0 ?
The solutions to the equation 4z+z^2+12=0 are z=-2+2sqrt(2)i,z=-2-2sqrt(2)i
Find the zeros of 4z+z^2+12=0
The zeros of 4z+z^2+12=0 are z=-2+2sqrt(2)i,z=-2-2sqrt(2)i