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Algebra · Quadratic-Equations

Solve x^2 + 1 = 0

x^{2} + 1 = 0

Step by step

  1. x^{2} + 1 = 0

    Start from the equation as given.

  2. a = 1,\quad b = 0,\quad c = 1

    Read off the coefficients of the standard form ax² + bx + c = 0.

  3. \Delta = b^2 - 4ac = (0)^2 - 4(1)(1) = -4

    It does not factor nicely, so use the discriminant Δ = b² − 4ac.

  4. x = \frac{-b \pm \sqrt{\Delta}}{2a} = \frac{0 \pm \sqrt{-4}}{2}

    Δ < 0, so the roots are a complex-conjugate pair. Substitute into the quadratic formula.

  5. x = i \quad\text{or}\quad x = - i

    Simplify each root.

Reveal the answer
x = i \quad\text{or}\quad x = - i