Question

solve; find all real and imaginary solutions in exact form. x^4-9x^2-10=0

Answer 1

maybe easier to start with
\[u^2-9u-10=0\] find the two solutions, then replace \(u\) by \(x^2\) and solve for \(x\)

Answer 2

find the dicriminent then the roots of 4x^2-2x+4=0

Answer 3

not to bad since \[u^2-9u-10\] factors as
\[(u-10)(u+1)\] so you can easily solve
\[(u-10)(u+1)=0\]

Answer 4

that makes sense!

Answer 5

thanks!

Answer 6

yw

Answer 7

so I got 10 and -1 but when you plug both of them back in, neither of them work

Answer 8

of course they do
they work for \[u^2-9u-10=0\] but not for the original equation
now you have to solve
\[x^2=10\] and also \(x^2=-1\)

Answer 9

ohhhh! I see ok

Answer 10

both are easy, the second one gives you the two complex solutions

Answer 11

yea, I see what I did wrong, I plugged it into the wrong equation. thanks!

Answer 12

so to find \[x^2=10\] and \[x^2=-1\] you have to take the square root of each side?