Data Sufficiency (DS) | Re: Is zp negative?

from statement -1: it's confirmed p is negative but not Z.
from statement - 2: it's not confirmed what are the signs of Pand Z.

from statement 1and 2.

p +z^4 = 14.

now we know p = negative. let say
p= -15.
then:
-15 + z^4 = 14
z^4 = 14 + 15
z^4 = 29
so z is always positive.
in this case answer is c.
please correct me if I am wrong.

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