Final answer:
The discriminant of the quadratic equation 5x² - 10x - 4 is 180, indicating that the equation has two distinct real roots.
Step-by-step explanation:
The equation given in the question, x² - 5x + 4x² - 5x - 4, simplifies to 5x² - 10x - 4. This is a quadratic equation in the form ax² + bx + c = 0. To find the discriminant of a quadratic equation, we use the formula Δ = b² - 4ac. Substituting the values for a, b, and c from the simplified equation, we get Δ = (-10)² - 4(5)(-4) = 100 + 80 = 180.
The discriminant provides us with information about the nature of the roots of the quadratic equation. Since the discriminant is positive, it indicates that there are two distinct real roots for the given quadratic equation.