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Mamont248 [21]
3 years ago
7

Write a polynomial function f of least degree that has rational coefficients, a leading coefficient of 1, and the zeros −3 and 5

+i.
Mathematics
1 answer:
love history [14]3 years ago
7 0

Answer:

<em>f(x) = x² (2+i)x-15-3i</em>

Step-by-step explanation:

Since the zeros of the equation are -3 and 5+i, hence the factors of the polynomial in x is (x+3) and (x-(5+i))

Multiplying both factors

f(x) =  (x+3)(x-(5+i))

f(x) = (x²-(5+i)x+3x -3(5+i))

f(x) = x² - (5+i- 3)x -15-3i

f(x) = x² (2+i)x-15-3i

<em>hence the required polynomial function in x is f(x) = x² (2+i)x-15-3i</em>

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