Question

Find all zeros in the equation.

x^4+8x^2-9=0

Can you please explain what steps to take, so I can do every other question in my practice problems? Thank you.

Answer 1

\[x^4+8x^2-9=0\] if it factors, use that.

Answer 2

if it is does not factor you can replace x by z^2 and solve
\[z^2+8z-9=0\] but i think this factors as
\[(x^2+9)(x^2-1)=0\] therefore
\[x^2+9=0\] or
\[x^2-1=0\]

Answer 3

if you are working over the real numbers, there is no solution to
\[x^2+9=0\] because
\[x^2\geq0\] and therefore it cannot be -9

Answer 4

and then
\[x^2-1=0\]
\[(x+1)(x-1)=0\]
\[x=1 \text { or } x = -1\] or you can write
\[x^2-1=0\implies x^2=1\implies x=\pm1\]

Answer 5

okay. thank you.

Answer 6

yw