Question

Write a polynomial function of minimum degree with real coefficients whose zeros include those listed. Write the polynomial in standard form.
4, -14, and 5 + 8i

Answer 1

Well, get to work!

f(x) = (x-4)(x+14)(x-(??))(x+(??))

You tell me the missing pieces!

Answer 2

5+8i and 5-8i

Answer 3

Fooled you. That would be exactly correct if I had written it exactly correctly. I'll try again and fill in your CORRECT answers.

f(x) = (x-4)(x+14)(x-(5+8i))(x-(5-8i))

That's all there is to it. So start multiplying to get the standard form.

Answer 4

i dont remember how to multiply out the imaginary part

Answer 5

There's nothing to remember. It is just like any other multiplication.

Do you know this? \((a+b)(a-b) = a^{2}-b^{2}\) That's what we're doing.

(x-(5+8i))(x-(5-8i)) = (x-5-8i)(x-5+8i)

Just multiply those trinomials. There's no secret. Just match up all the pieces.

Answer 6

im confused

Answer 7

Can you multiply these two numbers? 123*456?

Answer 8

yeah

Answer 9

i know how to do that

Answer 10

How did you do it?

6*3
6*2
6*1
5*3
4*2
5*1
4*3
4*2
4*1
In an organized fashion?

That is EXACTLY how to multiply the trinomial you are facing.