Question

Write a polynomial function of minimum degree with real coefficients whose zeros include those listed. Write the polynomial in standard form.

3, -13, and 5 + 4i

A f(x) = x4 - 8x3 - 12x2 + 400x - 1599
B f(x) = x4 - 200x2 + 800x - 1599
C f(x) = x4 - 98x2 + 800x - 1599
D f(x) = x4 - 8x3 + 12x2 - 400x + 1599

Answer 1

in general, a function has root (a) if (x - a) = 0

applying this logic to the problem, root of 3 gives you (x-3) and root of (-13) gives you (x+13)

it gets a little trickier once imaginary numbers are involved. complex roots come in conjugate pairs, so if 5 + 4i is a root, then 5 - 4i is a root as well. so that gives us (x - (5-4i)) and (x - (5+4i))

multiply all the parts of the function together, and re-write in standard form