Find a polynomial with integer coefficients that satisfies thegiven conditions U has degree 5 zeros 1/2, -1, and -i the leading coefficient is 4 the zero -1 has multiplicity 2

cochetezgh

cochetezgh

Answered question

2022-09-04

Find a polynomial with integer coefficients that satisfies thegiven conditions
U has degree 5
zeros 1/2, -1, and -i
the leading coefficient is 4
the zero -1 has multiplicity 2

Answer & Explanation

Griffin Dean

Griffin Dean

Beginner2022-09-05Added 13 answers

U ( x ) = ( x 2 + 1 ) ( x + 1 ) ( x + 1 ) ( 2 x 1 )
[expand]
U ( x ) = ( x 3 + x 2 + x + 1 ) ( 2 x 2 + x 1 )
U ( x ) = 2 x 5 + 3 x 4 + 2 x 3 + 2 x 2 1
[multiply entire function by 2, since the current leading coeff is 2 and the problem requires it to be 4]
U ( x ) = 4 x 5 + 6 x 4 + 4 x 3 + 4 x 2 2

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