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irina [24]
2 years ago
13

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

Mathematics
1 answer:
ElenaW [278]2 years ago
7 0

Answer:

f(x)=x^3 +4x^2 +16x +64

Step by step explanation:

\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

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