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Question:

For what value(s) of k will the expression p + $\frac{1}{9}\sqrt{p}$ + $k^2$ have equal roots.

Explanation:

For roots to be equal Discriminant should be 0

⇒ (1/9)² - 4 × 1 × k² = 0

⇒ 4k² = (1/9)²

⇒ k² =  (1/18)²

⇒ k = ± (1/18)

Hence, option (b).