The polynomial P in lowest degree given the following roots: 4, -3, 4i is x^3 - (4i+1)x^2+4(i-3)x + 48i
Given the roots of a polynomial such as 4, -3, 4i. The equivalent factors of the polynomial will be x-4, x+3 and x-4i
Taking the product of the factors
P(x) = (x-4)(x+3)(x-4i)
P(x) = (x^2+3x-4x-12)(x-4i)
P(x) = (x^2 - x - 12)(x-4i)
P(x) = x^3-4x^2i-x^2+4xi-12x+48i
P(x) = x^3 - (4i+1)x^2+4(i-3)x + 48i
Hence the polynomial P in lowest degree given the following roots: 4, -3, 4i is x^3 - (4i+1)x^2+4(i-3)x + 48i
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