Question

Find polynomial p(x). Assume lead coefficient is one

Degree 4, x=-1,x=2,x= i

I worked it out but did not get the correct answer

@precal

Answer 1

f(x) = a(x-c1)(x-c2)(x-c3)(x-c4)

Answer 2

What you're given are the four roots of the function. We just need to rewrite them in factor forms.

Answer 3

For instance, x=-1 in factor form is (x-(-1))=(x+1).

Answer 4

x=2 would be (x-2)

Answer 5

But then the x=i always come in pair.

(x-i) (x+i)

Answer 6

Putting them together, we should have...

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

Answer 7

Just now realized a = 1

Answer 8

So I got

(X+1)(x+2)(x^2+1)

Answer 9

Oh dang I just seen what I did ... I got the sign wrong on the 2

Thank you very much for your help.