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

The Correct Option is A

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

\(⇒16+4log_2A>0\)

\(⇒log_2A>−4\)

\(⇒A>2−4\)

\(⇒A>116\)