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

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

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

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

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1 + x + x^{2} = 0

x = - \frac{1}{2} + i \frac{3}{2}, x = - \frac{1}{2} - i \frac{3}{2}

Solution steps

1 + x + x^{2} = 0

Write in the standard form

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

x^{2} + x + 1 = 0

Solve with the quadratic formula

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

Simplify

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

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

Separate the solutions

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

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

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

The solutions to the quadratic equation are:

x = - \frac{1}{2} + i \frac{3}{2}, x = - \frac{1}{2} - i \frac{3}{2}

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

x^{2} - 10 x + 26

4 x^{2} - 64 = 17

x^{2} + 10 x + 32 = 0

(x - 9)^{2} = 13

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