Find the discriminant.
u2+4u+4=0
How many real solutions does the equation have?

To find the discriminant of the quadratic equation \( u^2 + 4u + 4 = 0 \), we use the discriminant formula:

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

For a quadratic equation in the form \( ax^2 + bx + c = 0 \), \( a \), \( b \), and \( c \) are the coefficients. Here, \( a = 1 \), \( b = 4 \), and \( c = 4 \).

### Step 1: Calculate the discriminant

\[
\Delta = (4)^2 - 4(1)(4) = 16 - 16 = 0
\]

### Step 2: Determine the number of real solutions

- If the discriminant (\( \Delta \)) is **greater than 0**, there are **two distinct real solutions**.
- If the discriminant (\( \Delta \)) is **equal to 0**, there is **one real solution** (a repeated root).
- If the discriminant (\( \Delta \)) is **less than 0**, there are **no real solutions** (the roots are complex).

Since \( \Delta = 0 \), the equation has **one real solution**.

Would you like further details or have any questions?

### Related Questions:
1. What is the discriminant of the equation \( 3x^2 + 2x - 1 = 0 \)?
2. How does the value of the discriminant affect the nature of the roots?
3. Solve the quadratic equation \( u^2 + 4u + 4 = 0 \) explicitly.
4. What is the quadratic formula, and how is it used to solve quadratic equations?
5. Can the discriminant be used to find complex roots? How?

### Tip:
When the discriminant equals zero, the quadratic equation can be factored into a perfect square trinomial, such as \( (u + 2)^2 = 0 \), indicating a repeated root.

Find the discriminant. u^2 + 4u + 4 = 0. How many real solutions does the equation have?

Explore how to find the discriminant of the quadratic equation u^2 + 4u + 4 = 0 using the discriminant formula Δ = b^2 - 4ac. This problem teaches how the discriminant determines the number of real solutions in quadratic equations. Perfect for students in Grades 9-10.

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