Let `f(x)` be a polynomial of degree 5 such that `f(|x|)=0` has 8 real distinct , Then number of real roots of `f(x)=0` is ________.

Explanation

To solve the problem, we need to analyze the given polynomial function \( f(x) \) and the implications of the equation \( f(|x|) = 0 \) having 8 distinct real roots.

### Step-by-Step Solution:

1. **Understanding the Equation**:
The equation \( f(|x|) = 0 \) means we are considering the polynomial \( f(x) \) evaluated at the absolute value of \( x \). This means that for every positive root \( r \) of \( f(x) \), there is also a corresponding negative root \( -r \).

2. **Roots of \( f(|x|) = 0 \)**:
Since \( f(|x|) = 0 \) has 8 distinct real roots, we can denote these roots as \( r_1, r_2, r_3, r_4, -r_1, -r_2, -r_3, -r_4 \). This gives us 4 positive roots and their corresponding 4 negative roots.

3. **Degree of the Polynomial**:
The polynomial \( f(x) \) is of degree 5. This means that the maximum number of real roots \( f(x) = 0 \) can have is 5.

4. **Analyzing the Roots**:
Since \( f(|x|) = 0 \) gives us 8 distinct roots (4 positive and 4 negative), we can conclude that \( f(x) \) must have some roots that are repeated or complex. However, since the degree of \( f(x) \) is 5, it can have at most 5 real roots.

5. **Conclusion**:
Given that \( f(x) \) can have at most 5 real roots and we have established that there are 4 distinct positive roots, we can conclude that \( f(x) = 0 \) must have exactly 4 real roots (the positive ones) and one additional root, which could be either a repeated root or a complex root.

Thus, the number of real roots of \( f(x) = 0 \) is **4**.

### Final Answer:
The number of real roots of \( f(x) = 0 \) is **4**.