How do you find all the zeros of #f(x) = x^4+ -7x^2 -144#?

Question

1467 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-03-11T02:47:39

#x = +-4, +-3i#

#f(x) - x^4 - 7x^2 - 144 # (Since # "+ -" = -#)

Let #z = x^2#
#f(x) = z^2 - 7z - 144#

To find all zeros set #f(x) = 0#
# z^2 - 7z - 144 = 0 #

Factorizing:
#(z+9) (z-16) = 0#

Therefore #z = -9 or 16#

But #z = x^2 -> x = +- sqrt(z)#

With #z = -9, x = +-3i#
And with #z = 16, x = +-4#