## anonymous one year ago Using the given zero, find all other zeros of f(x). -2i is a zero of f(x) = x4 - 32x2 - 144

1. anonymous

if $$2i$$ is a zero then so is $$-2i$$ therefore one factor is $$x+2i$$ and another is $$x-2i$$ multiply the factors, get $x^2+4$

2. anonymous

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

3. anonymous

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

4. anonymous

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

5. anonymous

those are my options

6. anonymous

once you find $$u$$ then replace it by $$x^2$$ and solve

7. anonymous

you know how to factor this ?

8. anonymous

hint, one of the factors is $$x^2+4$$

9. anonymous

10. anonymous

probably want me to check?

11. anonymous

12. anonymous

actually i change my mind probably not

13. anonymous

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

14. anonymous

36

15. anonymous

actually $$-36$$

16. anonymous

so this factors as $(x^2+4)(x^2-36)=0$

17. anonymous

final job it to solve $x^2-36=0$ for $$x$$

18. anonymous

6, -6

19. anonymous

yup

20. anonymous

Oh i see what i did wrong now, thanks!

21. anonymous

yw