Question

If (k + 2)x² − 2x + 1 = 0 has real roots then greatest value of k(∈ Z) is ______.

Options

• 1

• 3

• −1

• none of these

Answer 1

If (k + 2)x² − 2x + 1 = 0 has real roots then greatest value of k(∈ Z) is −1.

Explanation:

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.