If (k + 2)x² - 2x + 1 = 0 has real roots then greater value of k(∈ Z) is :

1. 1

2. 3

3. -1

4. none of these

Given,

Equation : (k + 2)x² - 2x + 1 = 0

Comparing (k + 2)x² - 2x + 1 = 0 with ax² + bx + c = 0 we get,

a = (k + 2), b = -2 and c = 1.

Since, roots are real,

∴ D ≥ 0

⇒ b² - 4ac ≥ 0

⇒ (-2)² - 4(k + 2)(1) ≥ 0

⇒ 4 - 4(k + 2) ≥ 0

⇒ 4 - 4k - 8 ≥ 0

⇒ -4k - 4 ≥ 0

⇒ 4k ≤ -4

⇒ k ≤ -1.

Thus, greatest value of k = -1.

Hence, option 3 is the correct option.