Question

If $x^2-4x+lo{g}_{\frac{1}{2}}a=0$ does not have two distinct real roots, then maximum value of a is

• A.
• B.
• C. -
• D. none of these

Answer 1

The correct option is B

$x^2-4x+lo{g}_{\frac{1}{2}}a=0$
$16-4lo{g}_{\frac{1}{2}}a\le 0$
$4\le lo{g}_{\frac{1}{2}}a$
$lo{g}_{\frac{1}{2}}a\ge lo{g}_{\frac{1}{2}}{\left(\frac{1}{2}\right)}^4$
$a\le \frac{1}{16}$ and $a\ge 0$
$a\in (0,\frac{1}{16}]$
Maximum value of $a=\frac{1}{16}$