Let z is complex number satisfying the equation z^2 −(3+i)z+m+2i=0, where mεR. Suppose the equation has a real root, then find the non real root?


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Question Number 49151 by rahul 19 last updated on 03/Dec/18

$L e t z i s c o m p l e x n u m b e r s a t i s f y i n g$ $t h e e q u a t i o n z^{2} - (3 + i) z + m + 2 i = 0,$ $w h e r e m ϵ R . S u p p o s e t h e e q u a t i o n$ $h a s a r e a l r o o t, t h e n f i n d t h e n o n r e a l r o o t ?$
	Answered by mr W last updated on 03/Dec/18

	$z_{1} = a = t h e r e a l r o o t$ $z_{2} = p + q i = t h e n o n r e a l r o o t$ $a + p + q i = 3 + i$ $a (p + q i) = m + 2 i$ $q = 1$ $a + p = 3$ $a q = 2 \Rightarrow a = 2$ $a p = m$ $\Rightarrow p = 1$ $\Rightarrow z_{2} = 1 + i$ $m = 2$
	Commented by rahul 19 last updated on 04/Dec/18
	thanks sir ��
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