Find a polynomial f(x) of degree 3 with real coefficents and following zeros. -4,4i

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02-06-2022
Mathematics

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Find a polynomial f(x) of degree 3 with real coefficents and following zeros. -4,4i

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Loneguyidn Loneguyidn · Answer 1 · 2022-06-02T03:41:29-04:00

Answer:

[tex]f(x)=x^3 +4x^2 +16x +64[/tex]

Step by step explanation:

[tex]\text{Given that, two roots are}~ -4~ \text{and}~ 4i.\\\\\text{Let,}\\\\~~~~~~~x = 4i\\\\\implies x^2 = 16i^2~~~~~~~;[\text{Square on both sides}]\\\\\implies x^2 = -16~~~~~~~~;[i^2 = -1]\\\\\implies x^2 +16 = 0\\\\\text{So,}~ x^2 +16~ \text{ is a factor of the 3 degree polynomial}.\\ \\ \text{The polynomial is ,}\\\\ f(x) = (x+4)(x^2 +16)\\\\~~~~~~~=x^3 +16x +4x^2 +64\\\\~~~~~~~=x^3 +4x^2 +16x +64[/tex]

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