Question

If the equation 5x² - 10x + log_1/5 a = 0 has real roots, then the minimum value of a is

(a) 1/5⁵

(b)  1/10¹⁰

(c)  1/5¹⁰

(d)  None of these

Answer 1

Correct option (a) 1/5⁵

5x² - 10x + log_1/5 a = 0 has real roots

⇒ 100 - 20log_1/5 a ≥ 0

⇒ log_1/5 a ≤ 5 = log_1/5(1/5)⁵

⇒ a > 0 and a ≥ 1/5⁵

Therefore, minimum value of a = 1/5⁵