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Explanation:

Given, |x2 – 4x - 13| = r
∴ x2 – 4x - 13 = ± r

We have two quadratic equations here but only three distinct roots it means one of the quadratic equations will have equal roots.

Case 1: x2 – 4x - 13 = r has equal roots, i.e., Discriminant = 0
⇒ x2 – 4x – 13 - r = 0 had D = 0

⇒ D = 16 – 4(-13 - r) = 0
⇒ 16 + 52 + 4r = 0
⇒ r = - 17 

Case 2: x2 – 4x - 13 = - r has equal roots, i.e., Discriminant = 0
⇒ x2 – 4x – 13 + r = 0 had D = 0

⇒ D = 16 – 4(-13 + r) = 0
⇒ 16 + 52 - 4r = 0
⇒ r = 17

Hence, option (c).

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