Find all the zeros of the equation -3x^4+27^2+1200=0 if you could show yourworkthat would be great :3

Question

asked Dec 16, 2019 64.5k views

1 Answer

Cduck · Answer 1 · 2019-12-22T18:53:38+0000

Divide both sides by -3, and replace
x^2 with
. Then

$-3x^4+27x^2+1200=0\iff y^2-9y-400=0$

Factorize the quadratic in
to get

$y^2-9y-400=(y+16)(y-25)=0\implies y=-16,y=25$

which in turn means

x^2=-16,x^2=25

But
$x^2\ge0$ for all real
, so we can ignore the first solution. This leaves us with

$x^2=25\implies x=\pm√(25)=\pm5$

If we allow for any complex solution, then we can continue with the solution we ignored:

$x^2=-16\implies x=\pm√(-16)=\pm i√(16)=\pm4i$