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
Correct Answer: C
Solution :
Since \[\operatorname{a}{{z}^{2}}+bz+c=0\] .... (1) and \[{{z}_{1}},\,\,{{z}_{2}}\] (roots of (1)) are such that Im \[({{z}_{1}}{{z}_{2}})\ne 0\]. Now, \[{{\operatorname{z}}_{1}}\,\,and\,\,{{z}_{2}}\] 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.
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