$$ - {\omega ^2} = A + B\omega ;\,\,\,\,\,\,\,\,\,\,1 + \omega = A + B\omega $$
$$ \Rightarrow A = 1,B = 1.$$
4
AIEEE 2011
MCQ (Single Correct Answer)
Let $$\alpha \,,\beta $$ be real and z be a complex number. If $${z^2} + \alpha z + \beta = 0$$ has two distinct roots on the line Re z = 1, then it is necessary that :
A
$$\beta \, \in ( - 1,0)$$
B
$$\left| {\beta \,} \right| = 1$$
C
$$\beta \, \in (1,\infty )$$
D
$$\beta \, \in (0,1)$$
Explanation
As real part of roots is $$1$$
Let roots are $$1 + pi,1 + q$$
$$\therefore$$ sum of roots $$ = 1 + pi + 1 + qi = - \alpha $$