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The question asks: "How many roots, real or complex, does the polynomial \( 7 + 5x^4 - 3x^2 \) have in all?"

This is a polynomial equation of degree 4 (due to the term \( 5x^4 \)), and according to the **Fundamental Theorem of Algebra**, the number of roots (both real and complex) of a polynomial is equal to its degree.

Since the degree of the polynomial is 4, the polynomial must have **4 roots** in total, whether real or complex.

Thus, the correct answer is **4**.

Would you like further details or have any questions? Here are some related questions:

1. What is the Fundamental Theorem of Algebra?
2. How can we determine how many roots are real versus complex?
3. How do complex roots appear in polynomials?
4. How do we solve a quartic (degree 4) polynomial?
5. Can a degree-4 polynomial have fewer than 4 real roots?

**Tip**: When counting roots, always consider both real and complex roots, as their sum must match the polynomial's degree.

How many roots, real or complex, does the polynomial 7 + 5x^4 - 3x^2 have in all?

Understand how to determine the total number of roots, both real and complex, for the polynomial 7 + 5x^4 - 3x^2. This problem explores key algebraic concepts like polynomial degrees and the Fundamental Theorem of Algebra. Suitable for high school students in Grades 9-12.

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