Find an equation

Question

Find an equation for f(x) , the polynomial of smallest degree with real coefficients such that f(x) breaks through the x-axis at 5 , breaks through the x-axis at 3 , has complex roots of -1-i and -i and passes through the point(0,88) .

Answer 1

f(x) = a(x - 5)(x - 3)(x + i)(x - 1)(x - 1 - i)(x + 1 + i)

To determine a, substitute 0 for x and 88 for f(0) and solve for a.