Question

Find the discriminant and the number of real roots for this equation x² - 3x - 8.

a) Discriminant = 17, Two real roots
b) Discriminant = -31, Two real roots
c) Discriminant = 41, Two real roots
d) Discriminant = -7, Two real roots

Answer 1

The discriminant of the given quadratic equation is 41, indicating that it has two real roots.

Step-by-step explanation:

The discriminant of a quadratic equation is given by the formula Δ = b² - 4ac, where a, b, and c are the coefficients of the equation. In this case, the equation is x² - 3x - 8 = 0. So, a = 1, b = -3, and c = -8. Substituting these values into the discriminant formula, we have: Δ = (-3)² - 4(1)(-8) = 9 + 32 = 41.

Since the discriminant Δ > 0 and the equation is a quadratic equation, it means that there are two real roots.