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2020 ASDAN Math Tournament
5
5
Part of
2020 ASDAN Math Tournament
Problems
(1)
2020 Team #5
Source:
10/24/2023
Two quadratic polynomials
A
(
x
)
A(x)
A
(
x
)
and
B
(
x
)
B(x)
B
(
x
)
have a leading term of
x
2
x^2
x
2
. For some real numbers
a
a
a
and
b
b
b
, the roots of
A
(
x
)
A(x)
A
(
x
)
are
1
1
1
and
a
a
a
, and the roots of
B
(
x
)
B(x)
B
(
x
)
are
6
6
6
and
b
b
b
. If the roots of
A
(
x
)
+
B
(
x
)
A(x) + B(x)
A
(
x
)
+
B
(
x
)
are
a
+
3
a + 3
a
+
3
and
b
+
1
2
b + \frac1 2
b
+
2
1
, then compute
a
2
+
b
2
a^2 + b^2
a
2
+
b
2
.
team test