Question:
Let A be a real number. Then the roots of the equation $x^{2}-4 x-\log _{2} A=0$ are real and distinct if and only if
- $A>1 / 16$
- $A>1 / 8$
- $A<1 / 16$
- $A<1 / 8$
Correct Answer: Option: 1
For quadratic equation $a x^{2}+b x+c=0$, the roots are real and distinct if $b^{2}-4 a c>0$
Given, $x^{2}-4 x-\log _{2} A=0$
$\therefore(-4)^{2}-4 \times 1 \times\left(-\log _{2} A\right)>0$
$\Rightarrow 16+4 \log _{2} A>0$
$\Rightarrow \log _{2} A>-4$
$\Rightarrow A>2^{-4}$
$\Rightarrow A>\frac{1}{16}$
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