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Let $A$ be a real number. Then the roots of the equation $x^{2}-4x-\log _{2}A=0$ are real and distinct if and only if

1. $A> \frac{1}{16}$
2. $A> \frac{1}{8}$
3. $A< \frac{1}{16}$
4. $A< \frac{1}{8}$

Ans should be an option (A)

For a quadratic equation to have real and distinct roots, it’s discriminant should be strictly greater than zero.

$\therefore$   $b^{2}-4ac\gt0$

$\Rightarrow$  $16-4(-\log_{2}A)\gt0$   $\Rightarrow$   $\log_{2}A\gt-4$   $\Rightarrow$   $A\gt \frac{1}{16}$

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