Pregunta
Question 5 (1 point) Match the number of zeros to each polynomial function \( \begin{array}{ll}4 \text { zeros } & \text { 1. } f(x)=3 x^{4}+4 x-8 \\ 7 & \text { 2. } f(x)=3 x^{4}-7 x^{2}-2 x^{7}-x+4\end{array} \)
Ask by Boyd Johnston. in the United States
Feb 03,2025
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**Match:**
- **4 zeros** → **1.** \( f(x) = 3x^{4} + 4x - 8 \)
- **7 zeros** → **2.** \( f(x) = 3x^{4} - 7x^{2} - 2x^{7} - x + 4 \)
Solución
Each polynomial has a number of zeros equal to its degree.
1. \( f(x) = 3x^{4} + 4x - 8 \) has **4 zeros**.
2. \( f(x) = 3x^{4} - 7x^{2} - 2x^{7} - x + 4 \) has **7 zeros**.
**Match:**
- **4 zeros** → **1.** \( f(x) = 3x^{4} + 4x - 8 \)
- **7 zeros** → **2.** \( f(x) = 3x^{4} - 7x^{2} - 2x^{7} - x + 4 \)
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Extra Insights
The first polynomial function, \( f(x)=3 x^{4}+4 x-8 \), is a degree 4 polynomial, which can have up to 4 zeros. However, it typically does not have 4 distinct real zeros due to potential complex roots. On the other hand, the second polynomial function, \( f(x)=3 x^{4}-7 x^{2}-2 x^{7}-x+4\), is a degree 7 polynomial and can have up to 7 zeros. Therefore, the correct matches would be: 1. 4 zeros - \( f(x)=3 x^{4}+4 x-8 \) 2. 7 zeros - \( f(x)=3 x^{4}-7 x^{2}-2 x^{7}-x+4 \)
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