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Contests
National and Regional Contests
USA Contests
MAA AMC
AMC 12/AHSME
1968 AMC 12/AHSME
13
13
Part of
1968 AMC 12/AHSME
Problems
(1)
Sum of Roots
Source: 1968 AHSME Problem #13
9/7/2011
If
m
m
m
and
n
n
n
are the roots of
x
2
+
m
x
+
n
=
0
x^2+mx+n=0
x
2
+
m
x
+
n
=
0
,
m
≠
0
m\ne0
m
=
0
,
n
≠
0
n\ne0
n
=
0
, then the sum of the roots is:
<
s
p
a
n
c
l
a
s
s
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
A
)
<
/
s
p
a
n
>
−
1
2
<
s
p
a
n
c
l
a
s
s
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
B
)
<
/
s
p
a
n
>
−
1
<
s
p
a
n
c
l
a
s
s
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
C
)
<
/
s
p
a
n
>
1
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
>
Undetermined
<span class='latex-bold'>(A)</span>\ -\dfrac{1}{2} \qquad <span class='latex-bold'>(B)</span>\ -1 \qquad <span class='latex-bold'>(C)</span>\ \dfrac{1}{2} \qquad <span class='latex-bold'>(D)</span>\ 1 \qquad <span class='latex-bold'>(E)</span>\ \text{Undetermined}
<
s
p
an
c
l
a
ss
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
A
)
<
/
s
p
an
>
−
2
1
<
s
p
an
c
l
a
ss
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
B
)
<
/
s
p
an
>
−
1
<
s
p
an
c
l
a
ss
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
C
)
<
/
s
p
an
>
2
1
<
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
>
Undetermined
quadratics
Vieta
AMC