Fermi
·
Concept Library
·
Courses
·
Books
·
Problems
·
Simulations
·
Math Wiki
·
High School
Fermi
›
Problems
The polynomial has integral coefficients with odd and even
MATHEMATICS · Subjective · A Level · Mathematics · Proof · Proof
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.
Related theory
Polynomials
Mathematical Logic
Browse the problem library