Final answer:
To find the absolute difference between the roots of the quadratic equation 2x^2 - mx + k = 0, use the quadratic formula to find the roots and then calculate the absolute value of their difference.
Step-by-step explanation:
The absolute difference between the roots of a quadratic equation can be found using the quadratic formula. For the equation 2x^2 - mx + k = 0, the quadratic formula is:
x = (-b ± √(b^2 - 4ac)) / (2a)
In this case, a = 2, b = -m, and c = k. We can substitute these values into the quadratic formula and solve for x1 and x2, the two possible roots. Then we can find the absolute difference between x1 and x2 by taking the absolute value of their difference:
abs(x1 - x2)