Question

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

Answer 1

f(x) = x² (2+i)x-15-3i

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

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