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!