Question

If the roots of the quadratic equation $ {{x}^{2}}-4x-lo{{g}_{3}}a=0 $ are real, then the least value of a is

• A. 81
• B. 1/81
• C. 1/64
• D. None of these

Answer 1

Answer: (B)

Since, the roots of the given equation are real. $ \therefore $ $ Disc>0\Rightarrow 16+4\text{ }lo{{g}_{3}}a\ge 0 $ $ \Rightarrow $ $ {{\log }_{3}}a\ge -4\Rightarrow a\ge {{3}^{-4}}\Rightarrow a\ge 1/81 $ Hence, the least value of a is $ 1/81 $ .