Question

Let A be a real number. Then the roots of the equation x² - 4x - log₂A = 0 are real and distinct if and only if
1. A < 1/16
2. A < 1/8
3. A > 1/16
4. A > 1/8

Answer 1

Correct Answer - Option 3 : A > 1/16

Calculation:

Condition for roots to be real and distinct of Ax² + Bx + C = 0

⇒ B² + 4AC > 0

According to question

⇒ (-4)² - 4 × 1 × (log₂A) > 0

⇒ 16 + 4log₂A > 0

⇒ log₂A⁴ > -16

After solving the log we get

⇒ A⁴ > 2^-16

⇒ A > 2^-4

⇒ A > 1/16

∴ The value of A > 1/16.