Algebra 2 homework, help plz!!!!!?

Question

What are rational, real, and complex zeros?

Answer 1

An example of a quadratic/cubic would help.

For a function p(x), a zero is defined to be a root of the corresponding equation
p(x) = 0

A rational root would be a solution which is a rational number.

EG: Let p(x) = x^2 - 4. Then x^2 - 4 = 0 means x = +/- 2, so
x = {-2, 2}, and these would be rational zeros.

A real root would include rationals roots plus radicals.

EG: Let p(x) = x^2 - 3. Then x^2 - 3 = 0 implies
x^2 = 3, and x = +/- sqrt(3).
x = {-sqrt(3), sqrt(3)} would both be real roots.

Complex zeros of p(x) would be complex roots of the equation p(x) = 0.

EG: Let p(x) = x^2 + 4. Then x^2 + 4 = 0, x^2 = -4, which would mean
x = +/- 2i.
Therefore, x = {2i, -2i}, and any complex zero is indicated by having an i (which is sqrt(-1)) in it.