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Find the fourth-degree polynomial function with zeros 3, -3, 3i, and - 3i. Write the function in factored form.

User Bryan Hanson
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1 Answer

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14 votes

By the zero product property, the expression is equivalent to zero if one of the factors of an expression is equal to zero.

Given each solution a. we can find a factor (x-a) of the polynomial and then multiply the factors to get the polynomial

x =3 The factor is : (x - 3)

x = -3 The factor is: (x + 3)

For 3i and -3i,

i = ±√-1

x = ±3i

let's take the square of both-side

x² = -9

The factor is : (x² +9 )

The polynomial p(x) = (x -3)(x+3)(x² +9)

User Seccpur
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