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

• A. $A>\frac{1}{16}$
• B. $A>\frac{1}{8}$
• C. $A<\frac{1}{16}$
• D. $A<\frac{1}{8}$

Answer 1

Answer: (A)

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

Answer 2

For quadratic equation $ax^2+bx+c=0$, the roots are real and distinct if $b^2−4ac>0$
We have, $x^2−4x−log_2A=0$
$∴(−4)^2−4×1×(−log_2A)>0$

$⇒16+4log_2A>0$

$⇒log_2A>−4$

$⇒A>2−4$

$⇒A>116$