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Mathematics
Problem
The polynomial
a
x
3
+
b
x
2
+
c
x
+
d
ax^3 + bx^2 + cx + d
a
x
3
+
b
x
2
+
c
x
+
d
has integral coefficients
a
,
b
,
c
,
d
a, b, c, d
a
,
b
,
c
,
d
with
a
d
ad
a
d
odd and
b
c
bc
b
c
even. Show that at least one zero of the polynomial is irrational.
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