Question

Write a polynomial function of least degree with integral coefficients that have the given zeros.
1) -1, -1, 2i
2) -3, 1, -3i
3) 0, -5, 3+i
4) -2, -3, 4-3i
the i is imaginary number

Answer 1

the given zeros -1, -1, 2i
so factors (x+1)(x+1)(x-2i)

Answer 2

@jim_thompson5910 what does "with integral coefficients" mean?

Answer 3

it means the coefficients are integers

Answer 4

if 2i is a root, then so is -2i

Answer 5

@jim_thompson5910 thanks

Answer 6

np

Answer 7

so it would be (x^2 + 2x + 1)(x^2 +4)?

Answer 8

(x+1)(x+1) expands to (x^2+2x+1)
(x-2i)(x+2i) expands to (x^2+4)

looks good

you need to expand it more though

Answer 9

the end answer is : x^4 + 2x^3 + 5x^2 + 8x + 4. I'm just not sure how to get there

Answer 10

@brittany23468 look at my first post

Answer 11

I was missing the other root the conjugate of (x-2i) which is (x + 2i)

Answer 12

now look at the subsequent post with the expansion

Answer 13

use this to help expand out (x^2 +4)(x^2 + 2x + 1)