Question

Write a polynomial function of minimum degree with real coefficients whose zeros include those listed. Write the polynomial in standard form. 4, -8, and 2 + 5i

Answer 1

the 4th root will be the conjugate of 2 + 5i - that is 2 - 5i

Answer 2

so you can write it in factor form and then expand to give standard form

Answer 3

I'm not sure how to expand out the third and fourth roots when it gets to 5i*-5i

Answer 4

i*i = -1
so 5i *-5i = -25* -1 = +25

Answer 5

remember that i = sqrt(-1)

Answer 6

Thank you so much, that helped out a lot!

Answer 7

yw

Answer 8

What about when it's x*5i?

Answer 9

subtract x from each root

4-x, -8-x, 2 + 5i -x, 2 - 5i -x

and mutliply them all together

P(x) = (4-x)(-8-x)(2+5i-x)(2-5i-x)


4-x
-8-x
-----
-32 +8x
-4x +x^2
-------------
-32 +4x +x^2



2+5i-x
2-5i-x
-------
4 +10i -2x
-10i -25i^2 +5ix
-2x -5ix +x^2
------------------------
4 -4x +25 +x^2


so, this gives us the product of:

(-32 +4x +x^2) (29 -4x +x^2)

Answer 10

Oh wow, thank you so much!

Answer 11

youre welcome. i find the just multiplying like we learned back in the 3rd grade really helps avoid alot of confusion in the process ... FOIL and the likes are just memory clutter if you ask me.