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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

- $A> \frac{1}{16}$
- $A> \frac{1}{8}$
- $A< \frac{1}{16}$
- $A< \frac{1}{8}$

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Ans should be option **(A)**

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

$\therefore$ $b^{2}-4ac\gt0$

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