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# CAT 2019 Quant Question with Solution 56

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

1. $A>1 / 16$
2. $A>1 / 8$
3. $A<1 / 16$
4. $A<1 / 8$

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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