Cases

${\Phi }_0$

${\Phi }_1$

${\Phi }_2$

${\Phi }_3$

$R_{hv}$

No. of sign change

No. of positive real roots

1

+

+

+

+

$R_{hv}<1$

0

0

2

+

+

+

−

$R_{hv}>1$

1

1

3

+

+

−

+

$R_{hv}<1$

2

0.2

4

+

+

−

−

$R_{hv}>1$

1

1

5

+

−

−

+

$R_{hv}<1$

2

0.2

6

+

−

−

−

$R_{hv}>1$

1

1

7

+

−

+

+

$R_{hv}<1$

2

0.2

8

+

−

+

−

$R_{hv}>1$

3

1.3