What are the solutions to the equation 3z^2+z+3=0 ?

The solutions to the equation 3z^2+z+3=0 are z=-1/6+i(sqrt(35))/6 ,z=-1/6-i(sqrt(35))/6

Find the zeros of 3z^2+z+3=0

The zeros of 3z^2+z+3=0 are z=-1/6+i(sqrt(35))/6 ,z=-1/6-i(sqrt(35))/6

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

z = - \frac{1}{6} + i \frac{35}{6}, z = - \frac{1}{6} - i \frac{35}{6}

Solution steps

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

Solve with the quadratic formula

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

Simplify

1^{2} - 4 \cdot 3 \cdot 3 : 35 i

z_{1, 2} = \frac{- 1 \pm 35 i}{2 \cdot 3}

Separate the solutions

z_{1} = \frac{- 1 + 35 i}{2 \cdot 3}, z_{2} = \frac{- 1 - 35 i}{2 \cdot 3}

z = \frac{- 1 + 35 i}{2 \cdot 3} : - \frac{1}{6} + i \frac{35}{6}

z = \frac{- 1 - 35 i}{2 \cdot 3} : - \frac{1}{6} - i \frac{35}{6}

The solutions to the quadratic equation are:

z = - \frac{1}{6} + i \frac{35}{6}, z = - \frac{1}{6} - i \frac{35}{6}

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What are the solutions to the equation 3z^2+z+3=0 ?
The solutions to the equation 3z^2+z+3=0 are z=-1/6+i(sqrt(35))/6 ,z=-1/6-i(sqrt(35))/6
Find the zeros of 3z^2+z+3=0
The zeros of 3z^2+z+3=0 are z=-1/6+i(sqrt(35))/6 ,z=-1/6-i(sqrt(35))/6