What is the discriminant of the quadratic equation x, squared, plus, 2, x, plus, 2, equals, 0x 
2
 +2x+2=0?

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

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

For the quadratic equation \( x^2 + 2x + 2 = 0 \), the coefficients are:
- \( a = 1 \)
- \( b = 2 \)
- \( c = 2 \)

Now, substituting these values into the discriminant formula:

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

\[
\Delta = 4 - 8 = -4
\]

So, the discriminant is \( \Delta = -4 \).

Since the discriminant is negative, this means the quadratic equation has **two complex (non-real) roots**.

Would you like further explanation or details on how to interpret the discriminant?

Here are 5 related questions you might find useful:
1. What is the significance of the discriminant in solving quadratic equations?
2. How do complex roots arise from a negative discriminant?
3. Can you explain how to find the roots of a quadratic equation when the discriminant is negative?
4. What happens when the discriminant equals zero in a quadratic equation?
5. How does the discriminant affect the shape of the parabola represented by a quadratic equation?

**Tip**: If the discriminant is positive, you will have real roots, but if it's negative, expect complex ones!

What is the discriminant of the quadratic equation x^2 + 2x + 2 = 0?

Discover how to calculate the discriminant of the quadratic equation x^2 + 2x + 2 = 0 using the discriminant formula Δ = b^2 - 4ac. Understand the implications of a negative discriminant and how it leads to complex roots. Suitable for students in Grades 9-10.

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