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CVM 2020
Problem 6
Problem 6
Part of
CVM 2020
Problems
(1)
CVM 2020 - Problem 6
Source: CVM 2020
7/16/2020
Let
P
(
x
)
P(x)
P
(
x
)
be a monic cubic polynomial. The lines
y
=
0
y = 0
y
=
0
and
y
=
m
y = m
y
=
m
intersect
P
(
x
)
P(x)
P
(
x
)
at points
A
A
A
,
C
C
C
,
E
E
E
and
B
B
B
,
D
D
D
,
F
F
F
from left to right for a positive real number
m
m
m
. If
A
B
=
7
AB = \sqrt{7}
A
B
=
7
,
C
D
=
15
CD = \sqrt{15}
C
D
=
15
, and
E
F
=
10
EF = \sqrt{10}
EF
=
10
, what is the value of
m
m
m
?
<
s
p
a
n
c
l
a
s
s
=
′
l
a
t
e
x
−
b
o
l
d
′
>
6.1.
<
/
s
p
a
n
>
<span class='latex-bold'>6.1.</span>
<
s
p
an
c
l
a
ss
=
′
l
a
t
e
x
−
b
o
l
d
′
>
6.1.
<
/
s
p
an
>
A monic polynomial is one that has a main coefficient equal to
1
1
1
. For example, the polynomial
P
(
x
)
=
x
3
+
5
x
2
−
3
x
+
7
P(x) = x^3 + 5x^2 - 3x + 7
P
(
x
)
=
x
3
+
5
x
2
−
3
x
+
7
is a monic polynomial Proposed by Lenin Vasquez, Copan
algebra
polynomial