Write the simplest polynomial function with the given roots: 2i, sqrt (3), 4.

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Mathematics

Stich

14 June, 03:50

Write the simplest polynomial function with the given roots: 2i, sqrt (3), 4.

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Alia · Answer 1

(x - 2i) (x + 2i) (x - √3) (x - 4) = (x^2 + 4) (x^2 - 4x - √3x + 4√3) = x^4 - 4x^3 - √3x^3 + 4√3x^2 + 4x^2 - 16x - 4√3x + 16√3 = x^4 - (4 + √3) x^3 + 4 (√3 + 1) x^2 - 4 (4 - √3) x + 16√3