explain how to find the domaion for polynomials?

Question

how to find the domain for radical equations?
how to find the domain for rational equations?

Answer 1

For radical equations, you are primarily concerned with where the expression under the radical is less than zero (if you are talking about square roots or other even-powered roots). Thus, solve an inequality for when the radicand >= 0. This will give you the domain.

Example: sqrt(2 - x) ---> solve: 2 - x >= 0
---> 2 >= x, or x <= 2.
So the domain (in interval notation) is: (-inf, 2].

For rational equations, you are primarily concerned with where the denominator equals zero. Thus, solve an equation for when the denominator = 0. The domain will be all real numbers, EXCEPT the ones that make the denominator zero.

Example: 2/(x^2 - 9) ---> solve: x^2 - 9 = 0
---> (x + 3)(x - 3) = 0
---> x = -3 and x = 3
So the domain (in interval notation) is: (-inf, -3) (-3, 3) (3, inf). Or in set notation: {x|x ~= -3 or 3} (~= means "not equal to")

Keep in mind that if a rational equation has a radical in the numerator, the domain of the rational equation will be restricted by the domain of the radical expression AND the domain of the denominator.

Example: sqrt(2 - x)/(x^2 - 9) ---> the domain is a combination of the previous two. Thus the domain is: (-inf, -3) (-3, 2]. The rest of the domain from the denominator is not included because the domain in the numerator does not exist beyond 2, so we cannot use it.
Well, hope this helps. Good luck.

Answer 2

Here you go: http://www.purplemath.com/modules/polydefs.htm