Published by:
CGP EDU Academic Team
Published on: August 12, 2026
Consider the equation 
, where 
is a complex variable and 
. Which of the following statements is true?
A
For real positive numbers 
, both roots are purely imaginary.
, both roots are purely imaginary. B
For all complex numbers 
, neither root is real.
, neither root is real. C
For all purely imaginary numbers 
, both roots are real and irrational.
, both roots are real and irrational. D
For real negative numbers 
, both roots are purely imaginary.
, both roots are purely imaginary.
Text Solution
Verified by ExpertsThe correct answer is:
D
Now, 
. If 
, then 
. So is false.
If 
is a negative real number, then 
is a negative real number.
So is true.
If 
, then 
, and the roots are 
and 
. So is false.
If 
(which is a complex number), then the roots are 0 and 
. So is false.
──────────────────────────────────────────────────────────────────────────────────────────
Prepare Smarter with CGP Edu
Get practice questions, solutions, and test series in one place.
Write a Review
Share your experience with this question and solution.
Commentary
Send your comment, doubt, correction, or feedback to admin.
Similar Questions
Explore conceptually related problems