## mskyeg 3 years ago Find the zeros of the function. State the multiplicity of any multiple zeros. y=x^4-8x^2+16

1. hartnn

have u tried this ?

2. mskyeg

ya im supposed to find the GCF but i don't think there is one so i dont know what to do

3. hartnn

GCF ? first put x^2=y what u get ?

4. mskyeg

why would x^2 equal y

5. hartnn

oh, it was just for simplification, u can put x^2 =t .... or z ..

6. hartnn

i didn't mean that y on left side...

7. mskyeg

square root both sides

8. hartnn

to find zeros of y=x^4-8x^2+16 u put y=0 x^4-8x^2+16=0 now if we put x^2 = t t^2 -8t +16 = 0 this is quadratic in t, can u solve it ?

9. mskyeg

so just use the quadratic formula

10. hartnn

or u can factor it .

11. mskyeg

the answer is -4 or 4 but the answer is supposed to be -2 or 2

12. mskyeg

how do i factor it

13. hartnn

yes, because x^2 is 4,4

14. hartnn

t^2-8t+16 = 0 t^2 -4t -4t +16 = 0

15. hartnn

ok?

16. hartnn

what u got t as ?

17. mskyeg

im sorry what?

18. hartnn

t^2 -4t -4t +16 = 0 can u solve for t ?

19. mskyeg

no thats why i asked

20. hartnn

t^2 -4t -4t +16 = 0 factor out t from first 2 terms , what u get ?

21. mskyeg

i mean t(t-8)+16=0

22. hartnn

t^2 -4t -4t +16 = 0 from this.... factor out t from 1st 2 terms....

23. mskyeg

thats what i thought i just did

24. hartnn

u factored t from t^2 -8t +16 = 0 i asked u to factor out t from t^2 -4t -4t +16 = 0

25. mskyeg

t(t-4-4)+16=0

26. hartnn

i mentioned 'from first two terms' ...

27. mskyeg

t(t-4-4t)+16=0

28. hartnn

t^2-4t-4t+16=0 t(t-4) -4 (t-4) = 0 did u get this ?

29. mskyeg

oh ok that makes sense

30. hartnn

t(t-4) -4 (t-4) = 0 (t-4)(t-4) =0 i factored t-4 from that, got this ?

31. mskyeg

how did u get rid of the t and -4 ouside the parentheses

32. hartnn

i did not get rid of that...its in the 2nd brackets '()' ... (t-4)

33. hartnn

if u are getting confused let a=t-4 t(t-4) -4 (t-4) = 0 ta-4a = 0 a(t-4)=0 now put back a= t-4 (t-4)(t-4) = 0 got this ?

34. mskyeg

ok

35. hartnn

so, t=4,4 which gives u x^2 = 4, 4

36. hartnn

so whats x = ?

37. mskyeg

x=2 and -2

38. mskyeg

x=+or - the square root of 4

39. hartnn

yes thats correct...x=2,-2 for x^2 =4 now since x^2 = 4,4 ....u get x= 2,2,-2,-2 that is a root =2 with muliplicity 2 and another root =-2 with multiplicity = 2