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MAA AMC
AMC 12/AHSME
1970 AMC 12/AHSME
11
Find the coefficients
Find the coefficients
Source: 1970 AHSME Problem 11
March 24, 2014
algebra
polynomial
Vieta
AMC
Problem Statement
If two factors of
2
x
3
−
h
x
+
k
2x^3-hx+k
2
x
3
−
h
x
+
k
are
x
+
2
x+2
x
+
2
and
x
−
1
x-1
x
−
1
, the value of
∣
2
h
−
3
k
∣
|2h-3k|
∣2
h
−
3
k
∣
is
<
s
p
a
n
c
l
a
s
s
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
A
)
<
/
s
p
a
n
>
4
<
s
p
a
n
c
l
a
s
s
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
B
)
<
/
s
p
a
n
>
3
<
s
p
a
n
c
l
a
s
s
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
C
)
<
/
s
p
a
n
>
2
<
s
p
a
n
c
l
a
s
s
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
D
)
<
/
s
p
a
n
>
1
<
s
p
a
n
c
l
a
s
s
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
E
)
<
/
s
p
a
n
>
0
<span class='latex-bold'>(A) </span>4\qquad<span class='latex-bold'>(B) </span>3\qquad<span class='latex-bold'>(C) </span>2\qquad<span class='latex-bold'>(D) </span>1\qquad <span class='latex-bold'>(E) </span>0
<
s
p
an
c
l
a
ss
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
A
)
<
/
s
p
an
>
4
<
s
p
an
c
l
a
ss
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
B
)
<
/
s
p
an
>
3
<
s
p
an
c
l
a
ss
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
C
)
<
/
s
p
an
>
2
<
s
p
an
c
l
a
ss
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
D
)
<
/
s
p
an
>
1
<
s
p
an
c
l
a
ss
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
E
)
<
/
s
p
an
>
0
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