Compute the absolute difference between the two real roots of the quadratic equation 2x^2 − 11x + 5 = 0.

Introduction / Context: The distance between the roots of a quadratic can be computed without solving for each root explicitly by using the identity |α − β| = sqrt((α + β)^2 − 4αβ). This leverages sum and product of roots from coefficients.

Given Data / Assumptions:

• Equation: 2x^2 − 11x + 5 = 0.
• Real roots exist (discriminant positive).

Concept / Approach: For ax^2 + bx + c = 0, α + β = −b/a and αβ = c/a. Then |α − β| = sqrt((α + β)^2 − 4αβ). This avoids computing α and β separately.

Step-by-Step Solution:

Verification / Alternative check: Solving explicitly via quadratic formula also yields roots whose difference is 4.5; the identity is quicker and exact.

Why Other Options Are Wrong: They correspond to common arithmetic slips (e.g., missing the division by a or miscomputing the constant term).

Common Pitfalls: Using sqrt(b^2 − 4ac)/a directly and forgetting to divide by |a|, which leads to the same value but often mishandled.

Final Answer: 4.5