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Contests
National and Regional Contests
India Contests
India Pre-Regional Mathematical Olympiad
2014 India PRMO
9
9
Part of
2014 India PRMO
Problems
(1)
2014 preRMO p9, a,b roots of x^2-kx+l=0, a+1/b,b+1/a roots of x^2-px+q=0
Source:
8/9/2019
Natural numbers
k
,
l
,
p
k, l,p
k
,
l
,
p
and
q
q
q
are such that if
a
a
a
and
b
b
b
are roots of
x
2
−
k
x
+
l
=
0
x^2 - kx + l = 0
x
2
−
k
x
+
l
=
0
then
a
+
1
b
a +\frac1b
a
+
b
1
and
b
+
1
a
b + \frac1a
b
+
a
1
are the roots of
x
2
−
p
x
+
q
=
0
x^2 -px + q = 0
x
2
−
p
x
+
q
=
0
. What is the sum of all possible values of
q
q
q
?
algebra
trinomial
roots