What are the solutions to the equation 3x^2+x+1=0 ?

The solutions to the equation 3x^2+x+1=0 are x=-1/6+i(sqrt(11))/6 ,x=-1/6-i(sqrt(11))/6

Find the zeros of 3x^2+x+1=0

The zeros of 3x^2+x+1=0 are x=-1/6+i(sqrt(11))/6 ,x=-1/6-i(sqrt(11))/6

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

x = - \frac{1}{6} + i \frac{11}{6}, x = - \frac{1}{6} - i \frac{11}{6}

Solution steps

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

Solve with the quadratic formula

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

Simplify

1^{2} - 4 \cdot 3 \cdot 1 : 11 i

x_{1, 2} = \frac{- 1 \pm 11 i}{2 \cdot 3}

Separate the solutions

x_{1} = \frac{- 1 + 11 i}{2 \cdot 3}, x_{2} = \frac{- 1 - 11 i}{2 \cdot 3}

x = \frac{- 1 + 11 i}{2 \cdot 3} : - \frac{1}{6} + i \frac{11}{6}

x = \frac{- 1 - 11 i}{2 \cdot 3} : - \frac{1}{6} - i \frac{11}{6}

The solutions to the quadratic equation are:

x = - \frac{1}{6} + i \frac{11}{6}, x = - \frac{1}{6} - i \frac{11}{6}

2 x = 5 x

2 x^{3} + x^{2} - 32 x - 16

∣ x - 6 ∣ = 14

x^{2} = 12 x - 52

x^{2} + 11 x + 30 \geq 0

What are the solutions to the equation 3x^2+x+1=0 ?
The solutions to the equation 3x^2+x+1=0 are x=-1/6+i(sqrt(11))/6 ,x=-1/6-i(sqrt(11))/6
Find the zeros of 3x^2+x+1=0
The zeros of 3x^2+x+1=0 are x=-1/6+i(sqrt(11))/6 ,x=-1/6-i(sqrt(11))/6