Question

O.o...write a polynomial function of least degree with integral coefficients that has the given zeros.
4i, 3, -3
a. f(x)=x^3-2x^2-19x+20
b. f(x)=x^4-10x^3+20x^2+40x-96
c. f(x)=x^4+7x^2-144
d. f(x)=x^5-x^4+13x^3-13x^2+36x-36

Answer 1

i think it has to be 4 degrees

Answer 2

just go like this and expand

(x+4i) (x+3) (x-3) and expand. no wait i think it will be 3 then.

Answer 3

but i heard somewhere that imaginers have to come in pairs. so it could be 4 degrees

Answer 4

yea - thats what i was going to say wouldnt the roots be 4i and -4i?

Answer 5

wouldnt that make the last term -144?

Answer 6

thats what i was thinking daijones..but i wasnt sure

Answer 7

i think so
well a doesn't have 4i as solution so it definately a 4 degree :D

Answer 8

that means its must be c

Answer 9

(x+4i) (x+3) (x-3) (x-4i) expand that :)

Answer 10

thanks for the help guys!!

Answer 11

x^4-144+7*x^2