contestada

Write a polynomial function of minimum degree with real coefficients whose zeros include those listed. Write the polynomial in standard form.

5, -3, and -1 + 3i

f(x) = x4 + 12.5x2 - 50x - 150
f(x) = x4 - 4x3 + 15x2 + 25x + 150
f(x) = x4 - 4x3 - 15x2 - 25x - 150
f(x) = x4 - 9x2 - 50x - 150

Respuesta :

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Answer:

[tex]f(x)=x^4-9x^2-50x-150[/tex]

Step-by-step explanation:

Let f(x) be the polynomial function of minimum degree with real coefficients whose zeros are 5, -3, and -1 + 3i be f(x).

By the complex conjugate property of polynomials, -1-3i is also a root of this polynomial.

Therefore the polynomial in factored form is [tex]f(x)=(x-5)(x+3)(x-(-1+3i))(x-(-1+3i))[/tex]

We expand to get:[tex]f(x)=(x^2-2x-15)(x^2+2x+10)[/tex]

We expand further to get:\

[tex]f(x)=x^4-9x^2-50x-150[/tex]

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