If the equation x² – m (2x – 4) + 5 = 0 has equal roots, which of the following is the value of m?

First, expand the given equation x^2 - m(2x - 4) + 5 = 0 into the standard form x^2 - 2mx + 4m + 5 = 0. Since the equation has equal roots, the discriminant (b^2 - 4ac) must equal zero, so we write (-2m)^2 - 4(1)(4m + 5) = 0. Simplifying this gives 4m^2 - 16m - 20 = 0, and dividing by 4 yields m^2 - 4m - 5 = 0. Factoring the quadratic gives (m - 5)(m + 1) = 0, so the valid positive value from the options is m = 5.

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