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For each of the following, find a polynomial function of the lowest degree with rational coefficients that have the given numbers as some of its zeros. a) zeros -5 and 2b) zeros 4, and -3i

Respuesta :

Answer:

[tex]f(x)=x^{2}+3x-10[/tex]

Explanations:

The standard equation of a polynomial as a function of "x" is expressed as:

[tex]f(x)=(x-a)(x-b)...(x-n)[/tex]

where a, b and n are the zero's of the polynomial.

Given the following zeros -5 and 2, the required polynomial will be expressed as:

[tex]\begin{gathered} f(x)=(x-(-5))(x-2) \\ f(x)=(x+5)(x-2) \end{gathered}[/tex]

Expand

[tex]\begin{gathered} f(x)=x(x)-2x+5x-5(2) \\ f(x)=x^2+3x-10 \end{gathered}[/tex]

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