What's the difference with these questions?

Question

1. find all the rational zeros of the function.
2. find all the real zeros of the function.

Answer 1

Tio find the zeros of a function is the same as finding the answer when you set the function equal to zero. For example, the zeroes of f(x) = x^2 - 4 is the same as the answers you get if you set x^2 - 4 = 0 and solve...
x = 2 or x = -2
The rational zeros are the x values so that f(x) = 0 and x is a rational number, that is, an integer, or a fraction (ratio of integers).
The real zeros are the x values so that f(x) = 0 and x is a real number. Such an answer can include square roots, cube roots, etc.
Note: every rational zero is also a real zero, but not every real zero is a rational zero.
For example, if you can solve a quadratic equation by factoring, you have found the rational zeroes.
If you cannot factor it you can still put it in the quadratic formula, and if the number under the sqrt (that is, the discriminant) comes out to be a positive number that does not have a whole number square root, then you have found irrational zeroes.
If the number under the discriminant comes out to be a negative number, then you have found complex zeroes.
The same applies for higher order equations, I've just kept the example to quadratics for ease in explaining.
Note: the rational numbers, and the irrational numbers together, make up the real numbers. The integers are a subset of the rational numbers.

Answer 2

The difference is the difference between rational and real. Rational means that you can write a number as a fraction. Real includes rational numbers and irrational numbers (like pi...can't be written as a fraction)