Question

form a polynomial f(x) with real coefficients having the given degree and zeros. degree 5; zeros 7; -i; -8+i

Answer 1

Do remember that a polynomial with real coefficients having \(a + bi\) as a root will also have \(a - bi\) as a root.

Answer 2

Right, they're called complex conjugates.

Also remember that if you have a polynomial with roots \(r_1,r_2,...,r_n\) you can write it in factored form as \[f(x) = a(x-r_1)(x-r_2)...(x-r_n)\] where \(a\) is an arbitrary constant (if you need it to pass through a specific point, otherwise 1)