For what positive k does x² − 2(k − 1)x + (k + 5) = 0 have equal roots?

4. D = 4(k − 1)² − 4(k + 5) = 0 gives k² − 3k − 4 = 0, so k = 4 or −1. The positive value is 4.

For what positive $k$ does $x^{2} - 2 (k - 1) x + (k + 5) = 0$ have equal roots?

Competition practiceAlgebra

D = 4 (k - 1)^{2} - 4 (k + 5) = 0

gives

k^{2} - 3 k - 4 = 0

, so

k = 4

or −1. The positive value is 4.

Answer: A) 4

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