How do you find the number of roots for #0=x^3-4x-48# using the fundamental theorem of algebra?
The degree of this polynomial is
A non-zero polynomial equation in one variable always has as many roots as its degree. They may be repeated and/or Complex, but it will have that many roots.
The highest degree term in
#x^3-4x-48 = (x-4)(x^2+4x+12)#
#x=(-b+-sqrt(b^2-4ac))/(2a) = (-4+-sqrt((-4)^2-(4xx1xx12)))/(2xx1)#
#=(-4+-sqrt(-32))/2 = -2+-2sqrt(2) i#
..that is a conjugate pair of Complex roots.