mskyeg
Find the zeros of the function. State the multiplicity of any multiple zeros.
y=x^4-8x^2+16
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hartnn
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have u tried this ?
mskyeg
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ya im supposed to find the GCF but i don't think there is one so i dont know what to do
hartnn
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GCF ?
first put x^2=y
what u get ?
mskyeg
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why would x^2 equal y
hartnn
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oh, it was just for simplification,
u can put x^2 =t .... or z ..
hartnn
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i didn't mean that y on left side...
mskyeg
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square root both sides
hartnn
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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 ?
mskyeg
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so just use the quadratic formula
hartnn
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or u can factor it .
mskyeg
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the answer is -4 or 4 but the answer is supposed to be -2 or 2
mskyeg
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how do i factor it
hartnn
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yes, because x^2 is 4,4
hartnn
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t^2-8t+16 = 0
t^2 -4t -4t +16 = 0
hartnn
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ok?
hartnn
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what u got t as ?
mskyeg
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im sorry what?
hartnn
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t^2 -4t -4t +16 = 0
can u solve for t ?
mskyeg
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no thats why i asked
hartnn
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t^2 -4t -4t +16 = 0
factor out t from first 2 terms , what u get ?
mskyeg
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i mean t(t-8)+16=0
hartnn
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t^2 -4t -4t +16 = 0
from this....
factor out t from 1st 2 terms....
mskyeg
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thats what i thought i just did
hartnn
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u factored t from t^2 -8t +16 = 0
i asked u to factor out t from t^2 -4t -4t +16 = 0
mskyeg
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t(t-4-4)+16=0
hartnn
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i mentioned 'from first two terms' ...
mskyeg
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t(t-4-4t)+16=0
hartnn
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t^2-4t-4t+16=0
t(t-4) -4 (t-4) = 0
did u get this ?
mskyeg
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oh ok that makes sense
hartnn
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t(t-4) -4 (t-4) = 0
(t-4)(t-4) =0
i factored t-4 from that, got this ?
mskyeg
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how did u get rid of the t and -4 ouside the parentheses
hartnn
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i did not get rid of that...its in the 2nd brackets '()' ... (t-4)
hartnn
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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 ?
mskyeg
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ok
hartnn
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so, t=4,4
which gives u
x^2 = 4, 4
hartnn
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so whats x = ?
mskyeg
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x=2 and -2
mskyeg
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x=+or - the square root of 4
hartnn
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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