Let n>1 be an integer and f(x)=xn+5xn-1+3.Show that f(x) is irreducible over Z.
Let n>1 be an integer and f(x)=xn+5xn-1+3.Show that f(x) is irreducible over Z.
Ankan Sen , 7 Years ago
Grade 10
Algebra> Let n>1 be an integer and f(x)=x n +5x n-...
1 Answersshubham
let a be integer, and a zeo of above expression , we apply contradiction
if
a=even
an=even=2p
an-1=2q
the expression=xn+5xn-1+3=2p+10q+3=which cannot be equal to 0 as even+even+odd=odd
if
a=odd
an=2p+1
an-1=2q+1
expression reduces to
2p+10q+9=which cannot be equal to zero = as e+e+o=o;
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