Write an equation for a polynomial function in factored form, with real coefficients, that has a double root at x = 3 and roots at x = 1 + 4i and x = −1 and passes through (0, 17).

Answer 1

P(x) = a(x - 3)(x - 3)(x + 1)(x - (1 + 4i))(x - (1 - 4i))

P(0) = 17

To determine value of a substitute 0 and 17 into the polynomial and simplify.