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Calculus 3
2018 PUMaC Live Round Calculus 3
2018 PUMaC Live Round Calculus 3
Source:
January 13, 2019
calculus
PuMAC
Live Round
Problem Statement
Let
R
(
f
(
x
)
)
\mathcal{R}(f(x))
R
(
f
(
x
))
denote the number of distinct real roots of
f
(
x
)
f(x)
f
(
x
)
. Compute
∑
a
=
1
1009
∑
b
=
1010
2018
R
(
x
2018
−
a
x
2016
+
b
)
.
\sum_{a=1}^{1009}\sum_{b=1010}^{2018}\mathcal{R}(x^{2018}-ax^{2016}+b).
a
=
1
∑
1009
b
=
1010
∑
2018
R
(
x
2018
−
a
x
2016
+
b
)
.
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