Solve 1+x/1+x^2 - ScanMath

Evaluate

1 + \frac{x}{1} + x^{2}

To find the roots of the expression,set the expression equal to 0

1 + \frac{x}{1} + x^{2} = 0

Divide the terms

1 + x + x^{2} = 0

Rewrite in standard form

x^{2} + x + 1 = 0

Substitute a= 1,b= 1 and c= 1 into the quadratic formula x = \frac{- b \pm b ^{2} - 4 a c}{2 a}

x = \frac{- 1 \pm 1 ^{2} - 4}{2}

Simplify the expression

More Steps

x = \frac{- 1 \pm - 3}{2}

Simplify the radical expression

More Steps

x = \frac{- 1 \pm 3 \times i}{2}

Separate the equation into 2 possible cases

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

Simplify the expression

More Steps

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

Simplify the expression

More Steps

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

Solution

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

Alternative Form

x_{1} \approx - 0.5 - 0.866025 i, x_{2} \approx - 0.5 + 0.866025 i

Simplify the expression