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Find an nth degree polynomial function with real coefficients satisfying the given conditions.

degree of the polynomial is 3; the zeros of the polynomial are 3 and i; and use f(2) = 25 to find an

Respuesta :

Step-by-step explanation:

Our roots are 3, and i so our roots form

will be

[tex](x - 3)(x - i)[/tex]

Since i is one root, it conjugate, must be the other.

so we have

[tex](x - 3)(x - i)(x + i)[/tex]

Simplify

[tex]( {x}^{2} + 1)(x - 3)[/tex]

[tex] {x}^{3} - 3 {x}^{2} + x - 3[/tex]

So the function is

[tex]x {}^{3} - 3 {x}^{2} + x - 3[/tex]

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