Question

Identify all of the roots of f(x) = x2 + 2x + 2.

Answer 1

Explanation:

We can use the quadratic formula to find the roots of the quadratic function f(x) = x^2 + 2x + 2:

x = (-b ± sqrt(b^2 - 4ac)) / 2a

Here, a = 1, b = 2, and c = 2. Substituting these values into the formula, we get:

x = (-2 ± sqrt(2^2 - 4(1)(2))) / 2(1)

x = (-2 ± sqrt(-4)) / 2

x = (-2 ± 2i) / 2

Simplifying, we get:

x = -1 ± i

Therefore, the roots of f(x) = x^2 + 2x + 2 are x = -1 + i and x = -1 - i. These are complex conjugate roots, which means that they cannot be expressed as real numbers.