The equation 16x^4 – 1 = 0 has how many positive solutions?

Answer 1

16x^4 - 1 = 0

16x^4 = 1

x^4 = 1/16

x2 = 1/4 or -1/4

x = 1/2, -1/2, i/2, or -i/2

one positive real solution, one negative real solution, and two imaginary solutions. The two imaginary are not positive, not negative, and not zero, not non-negative, not non-positive, just none of the above.

1/2 x 1/2 x 1/2 x 1/2

= 1/4 x 1/4 = 1/16

You might be tempted to refer to imaginary numbers as positive or negative, but they just aren't. Maybe if a complex number had a real and imaginary component and the real part was positive, you could call that complex number positive, but a purely imaginary number such as +i/2 is only "positive" in a very fictional imaginary sense. Some day maybe, but not yet. Mathematicians are picky about definitions. Everything they do depends on precise definitions, avoiding any ambiguity.