Help. ​

-3x⁴ + 27x² + 1200  =  0

 

First, let's divide each term by  -3  .

 

x⁴ - 9x² - 400  =  0

 

Now, notice that we can write  x⁴  as  (x²)² .

 

(x²)² - 9x² - 400  =  0

 

And this factors as...

 

(x² - 25)(x² + 16)  =  0            Set each factor equal to zero.

 

x² - 25  =  0          or          x² + 16  =  0

x²  =  25               or           x²  =  -16

 

Now we can solve each equation for  x  by taking the ± square root of both sides.

 

x  =  ± 5          or          x  =  ± 4i

 

So all the zeros are   5 ,  -5 ,  4i , and  -4i