Find the Domain z^4-21z^2-100=0

Problem

z4−21*z2−100=0

Solution

1. Identify the type of expression given. The expression is a polynomial equation in terms of the variable z

2. Recall the definition of the domain for a polynomial function or equation. A polynomial is defined for all possible values of the input variable unless specific constraints (like square roots of negative numbers or division by zero) are present.

3. Determine if any restrictions exist. Since there are no denominators containing z and no radicals with even indices, there are no values of z that make the expression undefined.

4. Conclude that the domain consists of all real numbers, or all complex numbers if the context allows for complex solutions. In standard algebra, the domain of a polynomial is the set of all real numbers.

Final Answer

Domain=(−∞,∞)

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