Megoldani a matematikai problémákat

Lépésről lépésre

1. x^{2} + 2 x + 5 = 0

   Start from the equation as given.

2. a = 1,\quad b = 2,\quad c = 5

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

3. \Delta = b^2 - 4ac = (2)^2 - 4(1)(5) = -16

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

4. x = \frac{-b \pm \sqrt{\Delta}}{2a} = \frac{-2 \pm \sqrt{-16}}{2}

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

5. x = -1 + 2 i \quad\text{or}\quad x = -1 - 2 i

   Simplify each root.