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MAA AMC
AMC 12/AHSME
1965 AMC 12/AHSME
22
22
Part of
1965 AMC 12/AHSME
Problems
(1)
Equality holds when...
Source:
1/11/2009
If
a
2
≠
0
a_2 \neq 0
a
2
=
0
and
r
r
r
and
s
s
s
are the roots of a_0 \plus{} a_1x \plus{} a_2x^2 \equal{} 0, then the equality a_0 \plus{} a_1x \plus{} a_2x^2 \equal{} a_0\left (1 \minus{} \frac {x}{r} \right ) \left (1 \minus{} \frac {x}{s} \right ) holds:
<
s
p
a
n
c
l
a
s
s
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
A
)
<
/
s
p
a
n
>
for all values of
x
,
a
0
≠
0
<span class='latex-bold'>(A)</span>\ \text{for all values of }x, a_0\neq 0
<
s
p
an
c
l
a
ss
=
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a
t
e
x
−
b
o
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′
>
(
A
)
<
/
s
p
an
>
for all values of
x
,
a
0
=
0
<
s
p
a
n
c
l
a
s
s
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
B
)
<
/
s
p
a
n
>
for all values of
x
<span class='latex-bold'>(B)</span>\ \text{for all values of }x
<
s
p
an
c
l
a
ss
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
B
)
<
/
s
p
an
>
for all values of
x
(C)
\ \text{only when }x \equal{} 0
(D)
\ \text{only when }x \equal{} r \text{ or }x \equal{} s
(E)
\ \text{only when }x \equal{} r \text{ or }x \equal{} s, a_0 \neq 0
algebra
polynomial
Vieta