Question

Write the polynomial in standard form and identify the zeros of the function and the x-intercepts of its graph. f(x)=(x-1)(x-1)(x+2i)(x-2i)

So far I have foiled and got the polynomial in standard form as :
f(x)=x^4-2x^3-5x^2-8x+4

How do I find the zeros?

Answer 1

@satellite73

Answer 2

@phi

Answer 3

@amistre64

Answer 4

your initial product form was:

f(x) = (x-1) (x-1) (x+2i) (x-2i)


correct?

Answer 5

Yes.

Answer 6

and, when you are multiply number together; and one of them is equal to zero; what does that do for the answer?

Answer 7

for example:

8*6*23*n = ? ; when n=0

Answer 8

It makes it zero.

Answer 9

thats the key to this problem then:

(x-1) (x-1) (x+2i) (x-2i) = 0 when any of the (...) parts equal zero

Answer 10

So I plug in numbers for x, and the zeros are whichever numbers, when plugged into the problem, make the equation = 0?

Answer 11

exactly, therefore

(x-1) = 0
when x=?

(x-1) = 0
when x=?

(x+2i) = 0
when x=?

(x-2i) = 0
when x=?

Answer 12

so my zeros are... 1, and + or - 2i?

Answer 13

yes

Answer 14

Oh, thank you.

Answer 15

youre welcome, and good luck ;)

Answer 16

:)