write a standard form polynomial function of least degree that has rational coefficients, a leading 1, and zeros of 4 and 3i

Answer 1

With real coefficients, the Conjugate Root Theorem tells us that if 3i is a root, so is -3i. Hence the polynomial has three roots: 4, 3i, and -3i. Use the factored form:

f(x) = a·(x-p)(x-q)(x-r)

1. a = leading coefficient = -1
2. p = one zero = 4
3. q = the second zero = 3i
4. r = the last zero = -3i

f(x) = -1·(x-4)(x-3i)(x-(-3i))

f(x) = -(x-4)(x-3i)(x+3i)

Multiply it out to put it into standard form.