Table 2.

Number of possible positive real roots of polynomial (5).

Case	A3	A2	A1	A0	Condition of ${\mathcal{R}}_0$	Possible positive root
1	+	+	+	-	${\mathcal{R}}_0>1$	1
2	+	+	-	-	${\mathcal{R}}_0>1$	1
3	+	-	+	-	${\mathcal{R}}_0>1$	1 or 3
4	+	-	-	-	${\mathcal{R}}_0>1$	1
5	+	+	+	+	${\mathcal{R}}_0<1$	0
6	+	+	-	+	${\mathcal{R}}_0<1$	0 or 2
7	+	-	+	+	${\mathcal{R}}_0<1$	0 or 2
8	+	-	-	+	${\mathcal{R}}_0<1$	0 or 2