51. \( -\sqrt{3} \) (multiplicity 2\( ),-1 \) (multiplicity 1 ), 0 (multiplicity 2\( ), \sqrt{3} \) (multiplicity 2\( ) \) 52. \( -\sqrt{5} \) (multiplicity 2 ), 0 (multiplicity 1 ), 1 (multiplicity 2 ), \( \sqrt{5} \) (multiplicity 2 )
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Each root \( r \) with multiplicity \( m \) contributes a factor of \( (x - r)^m \) to the polynomial. Let's break down each case: ### Problem 51: The roots given are: - \( -\sqrt{3} \) with multiplicity 2 - \( -1 \) with multiplicity 1 - \( 0 \) with Show more…
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