The discriminant of the quadratic equation 2x² - 4x + 3 = 0 is -8, which is less than zero, causing the roots to be complex conjugates rather than real numbers.

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Given the discriminant is negative, the quadratic formula yields complex solutions x = 1 ± (√2 / 2)i. This means the equation has no real roots, and the solutions exist only in the complex number domain. This fundamental property governs the nature of the roots regardless of location or other factors.

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