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

1 Answer
Mar 11, 2016

x = +-4, +-3i

Explanation:

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