SOLUTION: Find a polynomial with integer coefficients that satisfies the given conditions.
U has degree 5, zeros 1/2, −4, and −i, and leading coefficient 4; the zero −4 ha
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Question 1099280: Find a polynomial with integer coefficients that satisfies the given conditions.
U has degree 5, zeros 1/2, −4, and −i, and leading coefficient 4; the zero −4 has multiplicity 2.
Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
Each zero means the factored form of the polynomial has
as many factors of the form as the multiplicity of the zero.
That means that the factored form of the polynomial includes
For each complex zero, the conjugate complex number is also a zero.
That means that is also a zero, and that also appears as a factor.
So far we have the factors
,
accounting for the degree 5,
with for a leading coefficient.
We need to include as a factor to have 4 for a leading coefficient.
The polynomial is
= .
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