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Maths-

General

Easy

Question

If $x to the power of 2 end exponent minus 4 x plus l o g subscript 1 divided by 2 end subscript invisible function application a equals 0 text end text$ does not have two distinct real roots, then maximum value of a is

$\frac{1}{4}$
$\frac{1}{16}$
$- \frac{1}{4}$
None of these

The correct answer is: $fraction numerator 1 over denominator 16 end fraction$

$x to the power of 2 end exponent minus 4 x plus l o g subscript 1 divided by 2 end subscript invisible function application a equals 0$
$table row cell rightwards double arrow 16 minus 4 l o g subscript 1 divided by 2 end subscript invisible function application a less or equal than 0 end cell row cell rightwards double arrow 4 less or equal than l o g subscript 1 divided by 2 end subscript invisible function application a end cell row cell rightwards double arrow l o g subscript 1 divided by 2 end subscript invisible function application a greater or equal than l o g subscript 1 divided by 2 end subscript invisible function application open parentheses fraction numerator 1 over denominator 2 end fraction close parentheses to the power of 4 end exponent end cell end table$
$table row cell rightwards double arrow a less or equal than fraction numerator 1 over denominator 16 end fraction text end text text a end text text n end text text d end text text end text a greater than 0 end cell row cell rightwards double arrow a element of open parentheses 0 comma fraction numerator 1 over denominator 16 end fraction close square brackets end cell end table$
$text Therefore, maximum value of end text a equals fraction numerator 1 over denominator 16 end fraction text . end text$

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