Question

how do you solve 3t^6-48t^2=0

Answer 1

Factor out 3t^2

Answer 2

3t^2(t^4-16)

Answer 3

factor
3t^2(t^4 - 16) = 0
t = 0 , 2 , -2

Answer 4

Now you have the difference of two squares. Factor that.

Answer 5

How do you factor that out? I understand how you get that but there should be six answers

Answer 6

t = 0 , 2 , -2, 2i,-2i

Answer 7

\[t^4-16=(t^2-4)(t^2+4)=(t-2)(t+2)(t^2+4)\]

Answer 8

what happened to the 3t^2?

Answer 9

x=0 double root

Answer 10

I left it off because I thought you already recognized that it is a factor.

Answer 11

so how do you get the six answers by factoring is what im confused about

Answer 12

\[3t^2(t-2)(t+2)(t^2+4)\]

Answer 13

That is the completely factored form.

Answer 14

\[x_1=0,x_2=0,x_3=2,x_4=-2,x_5=2i,x_6=-2i\]

Answer 15

how do you get the six answers though. I know there should be six because the degree is six

Answer 16

there are 6 answers already!

Answer 17

How didyou get them though? I see and understand there are six but i dont know HOW you got them

Answer 18

\[3t^6-48t^2=0\]
\[3t^2(t^4-16)=0\]
\[3t^2(t-2)(t+2)(t^2+4)=0\]

Answer 19

If the product of factors is 0 then one of the factors has to be 0. so set each factor to 0 and solve

Answer 20

not sure how you are confused. Do you know how to find the *2* roots of
\[ t^2= 0\]
t= ±0
two solutions, 0 and 0

Answer 21

\[3t^2=0\]
\[t+2=0\]
\[t-2=0\]
\[t^2+4=0\]

Answer 22

if a*b=0 then a=0 or b=0

Answer 23

Okay, now I understand, thankyou so much