The polynomial x^2+3x+2 has only 3 zeros in Z6

Israel Hale

Israel Hale

Answered question

2022-07-28

The polynomial x 2 + 3 x + 2 has only 3 zeros in Z 6

Answer & Explanation

Marisa Colon

Marisa Colon

Beginner2022-07-29Added 18 answers

The polynomial x 2 + 3 x + 2 has only 3 zeros in Z 6
Solution: [ x 2 + 3 x + 2 ] = [ x 2 + 2 x + x + 2 ]
= [ x ( x + 2 ) + 1 ( x + 2 ) ]
= [ ( x + 2 ) ( x + 1 ) ] = [ 0 ]
Therefore, x = 2 = 4 and x = 1 = 5
Z 6 is not an integer domain therefore, is has 2 solutions to as = 0
i.e. 4 3 = 0 in Z 6
( x + 2 ) ( x + 1 ) = 4 3 x = 2 is solution
and also we have
3 2 = 0 in Z 6
( x + 2 ) ( x + 1 ) = 3 2 x = 1 is a solution
so,
Therefore x 2 + 3 x + 2 has 4 zeros in Z 6
There fore it is FALSE

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