Question

Find all the zeroes of the equation:
-3x^4 + 27x^2 + 1200 = 0

Answer 1

\[-3\left( x^4-9x^2-400 \right)=0\]
\[x^2=t,x^4=t^2\]
\[t^2-9t-400=0\]
1*-400=-400
25-16=9
25*-16=-400
\[t^2-\left( 25-16 \right)t-400=0\]
\[t^2-25t+16t-400=0\]
t(t-25)+16(t-25)=0
\[\left( t-25 \right)\left( t+16 \right)=0\]
t=-16,25
\[x^2=-16=16 \times -1=16 \iota^2,x^2-16 \iota^2=0\]
\[\left( x-4\iota \right)\left( x+4 \iota \right)=0,x=\pm \iota \]
\[x^2-25=0,\left( x+5 \right)\left( x-5 \right)=0,x=\pm 5\]

Answer 2

correction
it is \[x= \pm 4 \iota ,\]
4 is missing.

Answer 3

@sshayer sorry, I'm not sure I understand, whats the answer?

Answer 4

\[zeroes \ are \ x = \pm 5, \pm 4 \iota \]

Answer 5

wait, I'm sorry whats the thing at the end? It looks like an i without a dot?

Answer 6

Sorry, this is all new to me and I don't understand any of it

Answer 7

@marcelie @Kainui Do you guys have any ideas?

Answer 8

@Love_333 ... i is a complex number

Answer 9

\[\iota=\sqrt{-1}\]