Question

Find all rational, irrational, and complex zeros.

Answer 1

x^4-81

Answer 2

Can you factor it? It is the difference of two squares.

Answer 3

the best i coulve did was x^4-3^4

Answer 4

Think of it like this:
\[(x^2)^2-(9)^2\]

Answer 5

And use this:
\[a^2-b^2=(a-b)(a+b)\]

Answer 6

oh, so then it would be (x^2-9)(x^2-9)?

Answer 7

oh lemme do that really quick

Answer 8

Did you notice the + sign?

Answer 9

yes

Answer 10

And then x^2-9 will factor again.

Answer 11

so the rational is +3, and -3.

Answer 12

\[x^4-81=(x^2-9)(x^2+9)=(x-3)(x+3)(x^2+9)\]

Answer 13

Yes. And the complex?

Answer 14

umm. is it +3i and -3i?

Answer 15

It is. Good job!!

Answer 16

so are there any irrational ?

Answer 17

x^4 has 4 roots and we have found 4 roots. So what do you think?

Answer 18

oh. ic, thanks for your help.

Answer 19

yw