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2023 New Zealand MO
8
8
Part of
2023 New Zealand MO
Problems
(1)
P(x) = ax^4 - 8ax^3 + bx^2 - 32cx + 16c has 4 positive real roots
Source: 2023 NZMO - New Zealand Maths Olympiad Round 1 p8
9/2/2023
Find all non-zero real numbers
a
,
b
,
c
a, b, c
a
,
b
,
c
such that the following polynomial has four (not necessarily distinct) positive real roots.
P
(
x
)
=
a
x
4
−
8
a
x
3
+
b
x
2
−
32
c
x
+
16
c
P(x) = ax^4 - 8ax^3 + bx^2 - 32cx + 16c
P
(
x
)
=
a
x
4
−
8
a
x
3
+
b
x
2
−
32
c
x
+
16
c
polynomial
algebra