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

how do you do this? thank you :)

Question

Find all the zeros of the equation.
-3x^4+27x^2+1200=0

how do you do this? thank you :)

anonymous · Answer

Same way you do with a normal quadratic equation, except x^2 terms will be x^4 and x terms will be x^2.

anonymous · Answer

So you will split it 3 times: once to turn the quartic into 2 quadratics, and one split each for the quadratic components.

anonymous · Answer

Using wolfram alpha since I'm too lazy to get math, I first split the equation into:
(x^2 + 16)(x^2 -25)

anonymous · Answer

Eyeballing the first part, it's apparent that there are no real solutions to x^2 + 16 (if you are not experienced with this, apply the quadratic formula and see for yourself). I know that the roots will be +/- 4i

For x^2 -25, eyeballing it, I split it into (x -5)(x + 5). Again, if you aren't experienced, look up patterns in quadratic equations. The solutions to (x-5)(x+5) = 0 are +/- 5.

So our possible values for x end up being:
x = +/-4i or +/- 5

anonymous · Answer

thats a lot to take in haha. So its factoring as if a quadratic equation? but with more squares. (apologizing for grammar or lack there of, just trying to do some late night algebra)