Question

If the equation $5x^2-10x+lo{g}_{\frac{1}{5}}a=0$ has real roots then the minimum value of a is

• A. $\frac{1}{5^5}$
• B. $\frac{1}{{10}^{10}}$
• C. $\frac{1}{5^{10}}$
• D. none of these

Answer 1

The correct option is A $\frac{1}{5^5}$

$Solution:5x^2-10x+lo{g}_{\frac{1}{5}}a=0$ has real roots.
$100-20lo{g}_{\frac{1}{5}}a\ge 0$
$lo{g}_{\frac{1}{5}}a\le 5=lo{g}_{\frac{1}{5}}{\left(\frac{1}{5}\right)}^5$
$a\ge 0$ and $a\ge \frac{1}{5^5}$
minimum value of $a=\frac{1}{5^5}$