Math Problem Statement
Solution
In the question provided, you are given that one of the zeros of the polynomial function is , and you are asked to find another zero.
Key concept:
For polynomial functions with real coefficients, complex roots always occur in conjugate pairs. This means that if is a zero, its conjugate, , must also be a zero of .
Answer:
Another zero of is .
Would you like more details on this concept, or do you have any questions? Here are some related questions to explore:
- What are complex conjugates and why do they occur in pairs for polynomials with real coefficients?
- How would you find a polynomial if the given zeros include complex numbers like and ?
- What is the fundamental theorem of algebra, and how does it relate to the number of zeros a polynomial can have?
- How do you express a polynomial with complex roots in standard form?
- Can a polynomial have non-real complex roots if all its coefficients are real?
Tip: Always remember that the complex conjugate root theorem applies to polynomials with real coefficients, ensuring symmetry in their complex roots.
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Math Problem Analysis
Mathematical Concepts
Polynomial Functions
Complex Numbers
Complex Conjugates
Formulas
Complex Conjugate: If a + bi is a root, then a - bi is also a root in polynomials with real coefficients
Theorems
Complex Conjugate Root Theorem
Fundamental Theorem of Algebra
Suitable Grade Level
Grades 10-12
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