Question

Using the given zero, find all other zeros of f(x).

-2i is a zero of f(x) = x4 - 32x2 - 144

Answer 1

if \(2i\) is a zero then so is \(-2i\)
therefore one factor is \(x+2i\) and another is \(x-2i\)
multiply the factors, get
\[x^2+4\]

Answer 2

therefore this sucker factors as
\[x^4-32x^2-144=(x^2+4)(\text{something})\]

Answer 3

2i, 12, -12
2i, 6i, -6i
2i, 6, -6
2i, 12i, -12i

Answer 4

on the other hand you can solve this directly without knowing any zeros,
put \(u=x^2\) and solve
\[u^2-32u-144=0\] by factoring

Answer 5

those are my options

Answer 6

once you find \(u\) then replace it by \(x^2\) and solve

Answer 7

you know how to factor this ?

Answer 8

hint, one of the factors is \(x^2+4\)

Answer 9

is the answer a?

Answer 10

probably
want me to check?

Answer 11

yes please :)

Answer 12

actually i change my mind
probably not

Answer 13

\[x^4-31x-144=0\\
(x^2+4)(x^2+bx+c)=0\]can factor easily
how many times does \(4\) go in to \(144\)?

Answer 14

36

Answer 15

actually \(-36\)

Answer 16

so this factors as
\[(x^2+4)(x^2-36)=0\]

Answer 17

final job it to solve \[x^2-36=0\] for \(x\)

Answer 18

6, -6

Answer 19

yup

Answer 20

Oh i see what i did wrong now, thanks!

Answer 21

yw