FD =O, ie., 
Z+a;Z+a,=0 
—-a, + Vai —4a, 
has two roots 
11,2 = 5 ‘ (5.75) 
and these two roots £;, {2 Satisfy Eq. 5.67. Therefore, from the condition 
yl <1, Wl <1, 
1>a,>-1 (5.76) 
and, as “, <> < 1, 
(1 —p2) < 1p. 
Thus My +h2-H1 W2 <1 
and —a,;-a2< 1 
a;+a,>-1, (a,>-a;-1) (3.77) 
andas w,;>-—1, —w,<1, -1<u2<1 
— (1 +2) < (1 + p22). 
Thus — (M1 + 2) — Myla < 1 
and @j—a,<1, (@2>4a;-1). (5.78) 
Therefore, as shown in Fig. 5.15, on a 0 — a}, a2 plane, the region inside of A ABC is the 
stable zone for a; and a2. This stable zone is divided into two subzones. 
1. When Eq. 5.73 has two real roots or coincident equal roots, 
1 
a? > 4a, or a < qu (5.79) 
This is subzone [ I ] in Fig. 5.16. 
2. When Eq. 5.73 has unequal complex roots, 
1 
a?<4a2, or a> reat (5.80) 
This is subzone [ II ] in Fig. 5.16. 
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