Question

Find all the zeroes of the equation. Show all your work. -3x^4+27x^2+1200=0

Answer 1

There are two things you should do right away

Divide through by minus 3

Substitute another letter (say z) for x^2

Step One

-3x^4/-3 +27x^2/-3 + 1200/-3 = 0/-3

x^4 - 9x^2 - 400 = 0

Step 2

Let z = x^2

(x^2)^2 - 9(x^2) - 400 = 0

z^2 - 9z^2 - 400 = 0

Step 3

By factoring solve for z

(z - 25)(z + 16) = 0

z = 25

x^2 = 25

x =  +/- 5

============

z + 16 = 0

z = - 16

x^2 = - 16

x = sqrt(-16)

x = +/- 4i

I've included a graph to show that the zeros are correct.