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AMC 10
2005 AMC 10
16
Roots of a quadratic
Roots of a quadratic
Source:
February 9, 2006
quadratics
algebra
Problem Statement
The quadratic equation
x
2
+
m
x
+
n
=
0
x^2+mx+n=0
x
2
+
m
x
+
n
=
0
has roots that are twice those of
x
2
+
p
x
+
m
=
0
x^2+px+m=0
x
2
+
p
x
+
m
=
0
, and none of
m
m
m
,
n
n
n
, and
p
p
p
is zero. What is the value of
n
p
\frac{n}{p}
p
n
?
(A)
1
(B)
2
(C)
4
(D)
8
(E)
16
\text{(A)} \ 1 \qquad \text{(B)} \ 2 \qquad \text{(C)} \ 4 \qquad \text{(D)} \ 8\qquad \text{(E)} \ 16
(A)
1
(B)
2
(C)
4
(D)
8
(E)
16
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