Question

Find the greatest value of k ∈ N for which the equation x² − 4x + k = 0 has distinct real roots.

Options

• −4

• 3

• 1

• 4

Answer 1

3

Explanation:

Given,

x² - 4x + k = 0

Comparing x² − 4x + k = 0 with ax² + bx + c = 0 we get,

a = 1, b = −4 and c = k.

Since roots are distinct and real,

∴ D > 0

⇒ b² − 4ac > 0

⇒ (−4)² − 4(1)(k) > 0

⇒ 16 − 4k > 0

⇒ 16 > 4k

⇒ `16/4` > k

⇒ k < 4

Since k ∈ N,

Possible natural numbers less than 4 are: 1, 2, 3

The greatest value is: 3