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The problem asks to determine the range of values for the constant \( a \) such that the quadratic equation \( 2x^2 + ax + a = 0 \) has complex (imaginary) roots.

### Step-by-Step Solution

1. **Identify the Quadratic Equation:**

   The quadratic equation is:

   \[
   2x^2 + ax + a = 0
   \]

2. **Determine When the Roots are Complex:**

   For a quadratic equation \( ax^2 + bx + c = 0 \), the roots are complex if the discriminant \( \Delta = b^2 - 4ac \) is less than 0.

   Here, \( a = 2 \), \( b = a \), and \( c = a \).

   So, the discriminant is:

   \[
   \Delta = a^2 - 4 \cdot 2 \cdot a = a^2 - 8a
   \]

3. **Find the Condition for Complex Roots:**

   For complex roots, the discriminant must be less than 0:

   \[
   a^2 - 8a < 0
   \]

   Factor the quadratic inequality:

   \[
   a(a - 8) < 0
   \]

4. **Solve the Inequality:**

   To solve this inequality, find the critical points where the expression equals 0:

   \[
   a = 0, \quad a = 8
   \]

   Now, analyze the sign of the expression \( a(a - 8) \) in the intervals defined by these points:

   - For \( a < 0 \), \( a(a - 8) > 0 \)
   - For \( 0 < a < 8 \), \( a(a - 8) < 0 \)
   - For \( a > 8 \), \( a(a - 8) > 0 \)

   The expression \( a(a - 8) < 0 \) when \( 0 < a < 8 \).

5. **Conclusion:**

   The range of \( a \) for which the quadratic equation has complex roots is:

   \[
   \boxed{0 < a < 8}
   \]

### Answer:

The values that should be filled in the boxes are:

- For the left box (イ), the value is \( 0 \).
- For the right box (オ), the value is \( 8 \).

Would you like more details on any of these steps, or do you have any further questions?

### Related Questions:
1. What is a discriminant and how is it used to determine the nature of roots?
2. How do you solve quadratic inequalities like \( a^2 - 8a < 0 \)?
3. What are some examples of quadratic equations with complex roots?
4. How does the coefficient of \( x^2 \) affect the range of \( a \) for complex roots?
5. What is the graphical representation of complex roots in a quadratic equation?

### Tip:
When solving quadratic inequalities, always find the critical points and analyze the intervals they create on a number line.

次の2次方程式の解の種類を判別せよ。 2次方程式 2x^2 + ax + a = 0 が虚数解をもつとき、定数 a の値の範囲は、□ < a < □ である。

Learn how to determine the range of values for constant a such that the quadratic equation 2x^2 + ax + a = 0 has complex roots. This problem covers key algebraic concepts such as the discriminant and quadratic equations. Suitable for students in Grades 9-11.

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