Give the nature of roots of x²+5x+10=0​

Answer:Here's how to determine the nature of the roots of the quadratic equation x² + 5x + 10 = 0: 1. Use the Discriminant The discriminant (Δ) of a quadratic equation in the form ax² + bx + c = 0 is calculated as: Δ = b² - 4ac - If Δ > 0: The equation has two distinct real roots.- If Δ = 0: The equation has one real root (a double root).- If Δ < 0: The equation has two complex roots (conjugate pairs). 2. Apply to the Equation In our equation, a = 1, b = 5, and c = 10. Let's calculate the discriminant: Δ = 5² - 4 * 1 * 10 = 25 - 40 = -15 3. Interpretation Since Δ = -15, which is less than 0, the equation x² + 5x + 10 = 0 has two complex roots.

Answered by chaellorticio | 2024-09-03