Corollary 4.27.
Assuming that:
f
,
g
are real rooted of degree
n
have a common interlacing
Then
for all
t
∈
[
0
,
1
]
min
{
maxroot
(
f
)
,
maxroot
(
g
)
}
≤
maxroot
(
t
f
(
x
)
+
(
1
−
t
)
g
(
x
)
)
.