The discriminant \( \Delta \) of a quadratic equation \( ax^2 + bx + c = 0 \) is given by the formula:

\[
\Delta = b^2 - 4ac
\]

For the equation \( 2x^2 + 4x + 4 = 0 \), we have:

- \( a = 2 \)
- \( b = 4 \)
- \( c = 4 \)

Now, let's substitute these values into the discriminant formula:

\[
\Delta = 4^2 - 4(2)(4) = 16 - 32 = -16
\]

Thus, the discriminant is \( \Delta = -16 \).

### Interpretation:
Since the discriminant is negative, the quadratic equation has no real solutions; instead, it has two complex solutions.

Would you like to discuss the complex roots or further details?

### Related Questions:
1. How do you find the roots of a quadratic equation when the discriminant is negative?
2. What is the significance of the discriminant being positive, zero, or negative?
3. Can the quadratic formula be used to solve equations with complex roots?
4. How does completing the square work for equations with complex roots?
5. How do quadratic equations relate to the parabolas in a graph?

### Tip:
When the discriminant is negative, the quadratic equation has two complex conjugate roots.

Evaluate the discriminant, 2x^2 + 4x + 4 = 0

Learn how to evaluate the discriminant of the quadratic equation 2x^2 + 4x + 4 = 0. This step-by-step solution covers essential algebraic concepts, including the discriminant formula and its significance in determining the nature of roots. Suitable for students in Grades 8-10.

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