Question

find the least degree of a polynomial equation with roots -1, 3, and +-3i

I have no idea how to solve this. Can anyone help explain it to me?

Answer 1

There are four roots and therefore the least degree will be 4 (That is x^4 + .... )

If a is a root it means (x-a) is a factor.

So to get the polynomial, just multiply: (x+1)(x-3)(x-3i)(x+3i)

Multiply the last two factors first to get rid of the i. Also, make use of the identity:
(a+b)(a-b) = a^2 - b^2 when multiplying the last two factors.

Answer 2

so

(x+1)(x-3)(x^2-9)?

Answer 3

I^2 = -1 and so try again.

Answer 4

would the last term be x^2+9 then?

Answer 5

(x-3i)(x+3i)

foil it
x times x is x^2
-3i times 3i is -3i^2? or would you break it out into -3 times 3 and -i times i

either way -i times i is 1, because i times i is -1 right

Answer 6

(-3i) * (3i) = -9(i^2) = -9(-1) = +9
(x-3i)(x+3i) = x^2 + 9
Multiply that by (x+1) and then by (x-3).
Arrange the polynomial from the highest degree to the lowest degree.