If I have a polynom p with p(a)=0 , how to construct a polynom q with q(a^(−1))=0 .

Chelsea Lamb

Chelsea Lamb

Answered question

2022-09-20

If I have a polynom p with p ( a ) = 0, how to construct a polynom q with q ( a 1 ) = 0

Answer & Explanation

Triston Donaldson

Triston Donaldson

Beginner2022-09-21Added 10 answers

If
p ( x ) = p n x n + + p 1 x + p 0 ,
you have
0 = p n a n + + p 1 a + p 0 .
Now multiply this by a n to get that the polynomial
q ( x ) = p 0 x n + p 1 x n 1 + + p n
has a 1 as a root.

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