CAT 2019 Slot 2 QA Question & Solution

AlgebraMedium

Question

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

Options

$A > \frac{1}{16}$

$A < \frac{1}{16}$

$A < \frac{1}{8}$

$A > \frac{1}{8}$

Solution

The roots of $x^2 - 4x - log_{2}{A} = 0$ will be real and distinct if and only if the discriminant is greater than zero

16+4*$log_{2}{A}$ > 0

$log_{2}{A}$ > -4

A> 1/16