Question

The root of the equation \[ 2(1+i)x^2-4(2-i)x-5-3i=0 \] which has greater modulus is

• A. \(\dfrac{3-5i}{2}\)
• B. \(\dfrac{5-3i}{2}\)
• C. \(\dfrac{3-i}{2}\)
• D. none

Hint:

Check \(|c/a|\) before solving roots fully.

Answer 1

The Correct Option is D

Step 1: For quadratic \(ax^2+bx+c=0\), roots have equal modulus iff \(|c/a|=1\).
Step 2: \[ \frac{|c|}{|a|}=\frac{\sqrt{34}}{2\sqrt2}\neq1 \]
Step 3: Hence none of the given roots satisfies the condition.