Complex Numbers And Quadratic Equations question 699
Question: If $ z_1,z_2 $ are the roots of the quadratic equation $ az^{2}+bz+c=0 $ such that $ Im(z_1,z_2)\ne 0 $ then
Options:
A) a, b, c are all real
B) at least one of a, b, c is real
C) at least one of a, b, c is imaginary
D) all of a, b, c are imaginary
Show Answer
Answer:
Correct Answer: C
Solution:
Since $ az^{2}+bz+c=0 $ …. (1) and $ z_1,z_2 $ (roots of (1)) are such that Im $ (z_1z_2)\ne 0 $ . Now, $ z_1 $ and $ z_2 $ are not conjugates of each other. Complex roots of (1) are not conjugate of each other. Coefficient a, b, c cannot all be real; at least one of a, b, c, is imaginary.
BETA
