JEE MATHEMATICS MCQ: COMPLEX NUMBERS

1 Easy

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Analyzing +4 | -1

Let

\alpha

and

\beta

be real and

z

be a complex number. If

z^2+\alpha z+\beta=0

has two distinct roots on the line

\operatorname{Re}(z)=1

, then it is necessary that

View answer and explanation

Correct option: C

\beta \in(1, \infty)

Option C (

\beta \in(1, \infty)

) is correct because the product of the roots, which is

\beta

, must be greater than 1 due to the roots being distinct and lying on Re(z) = 1.

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