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2011 Kosovo National Mathematical Olympiad
1
KMO #1 (Grade 10) [p,q rational numbers]
KMO #1 (Grade 10) [p,q rational numbers]
Source:
March 13, 2011
algebra proposed
algebra
Problem Statement
Suppose that the roots
p
,
q
p,q
p
,
q
of the equation
x
2
−
x
+
c
=
0
x^2-x+c=0
x
2
−
x
+
c
=
0
where
c
∈
R
c \in \mathbb{R}
c
∈
R
, are rational numbers. Prove that the roots of the equation
x
2
+
p
x
−
q
=
0
x^2+px-q=0
x
2
+
p
x
−
q
=
0
are also rational numbers.
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