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

Question

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

hartnn · Answer

have u tried this ?

anonymous · Answer

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

hartnn · Answer

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

anonymous · Answer

why would x^2 equal y

hartnn · Answer

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

hartnn · Answer

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

anonymous · Answer

square root both sides

hartnn · Answer

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 ?

anonymous · Answer

so just use the quadratic formula

hartnn · Answer

or u can factor it .

anonymous · Answer

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

anonymous · Answer

how do i factor it

hartnn · Answer

yes, because x^2 is 4,4

hartnn · Answer

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

hartnn · Answer

ok?

hartnn · Answer

what u got t as ?

anonymous · Answer

im sorry what?

hartnn · Answer

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

anonymous · Answer

no thats why i asked

hartnn · Answer

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

anonymous · Answer

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

hartnn · Answer

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

anonymous · Answer

thats what i thought i just did

hartnn · Answer

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

anonymous · Answer

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

hartnn · Answer

i mentioned 'from first two terms' ...

anonymous · Answer

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

hartnn · Answer

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

anonymous · Answer

oh ok that makes sense

hartnn · Answer

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

anonymous · Answer

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

hartnn · Answer

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

hartnn · Answer

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 ?

anonymous · Answer

ok

hartnn · Answer

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

hartnn · Answer

so whats x = ?

anonymous · Answer

x=2 and -2

anonymous · Answer

x=+or - the square root of 4

hartnn · Answer

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