Find All Complex Zeros of the Polynomial Function $$f ( x ) = x ^ { 4 } - 9$$

question 488

Multiple Choice

Find all complex zeros of the polynomial function. Give exact values. List multiple zeros as necessary.
- $$f ( x ) = x ^ { 4 } - 9$$

• A) \(\sqrt { 3 } , - \sqrt { 3 } , 3 i , - 3 i\)
• B) \(\sqrt { 3 } , - \sqrt { 3 }\)
• C) \(\sqrt { 3 } , \sqrt { 3 } \mathrm { i }\)
• D) \(\sqrt { 3 } , - \sqrt { 3 } i , \sqrt { 3 } i , - \sqrt { 3 }\)

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Definitions:

Real Solutions

The set of all real numbers that satisfy an equation.

Quadratic Equation

An equation of the form ax^2 + bx + c = 0, where a, b, and c are constants, and a ≠ 0.

Square Root Property

A principle that relates the square of a number to its square root, often used to solve equations.

Square Root Property

A principle that states if \(x^2 = n\), then \(x\) is equal to the positive or negative square root of \(n\).