The discriminant of x^2 + 2x + 5 is equal to which value?

• A. -20
• B. 16
• C. 0
• D. -16

Answer: (D)

Discriminant tells you how many real solutions a quadratic has. It’s calculated as Δ = b^2 − 4ac.

For x^2 + 2x + 5, a = 1, b = 2, c = 5. So Δ = 2^2 − 4·1·5 = 4 − 20 = −16.

Because the discriminant is negative, there are no real roots—the solutions are complex numbers (they come in conjugate pairs). The discriminant value here is −16.