Solve following equation: $-x^2 + x - 2 = 0$
- $\dfrac{1\pm \sqrt{7}i}{2}$
- $\dfrac{-1\pm \sqrt{7}i}{2}$
- $\dfrac{2\pm \sqrt{7}i}{2}$
- $\dfrac{-2\pm \sqrt{7}i}{2}$
Reveal answer
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A
Correct answer
Explanation
For -x^2 + x - 2 = 0, multiply by -1 to get x^2 - x + 2 = 0. Using the quadratic formula x = (-b +/- sqrt(b^2 - 4ac)) / 2a, we get x = (1 +/- sqrt(1 - 8)) / 2 = (1 +/- sqrt(-7)) / 2 = (1 +/- i*sqrt(7)) / 2.
AI explanation
To solve the quadratic equation -x^2 + x - 2 = 0, we use the quadratic formula x = [-b +/- sqrt(b^2 - 4ac)] / 2a with the coefficients a = -1, b = 1, and c = -2. Substituting these values into the formula gives x = [-1 +/- sqrt(1^2 - 4(-1)(-2))] / (2 * -1). Simplifying the discriminant gives 1 - 8 = -7, so the roots are (-1 +/- sqrt(-7)) / -2. This further simplifies to (1 +/- sqrt(7)i) / 2.