Solution:
Given equation is 2x² + 5x + m = 0
Let α and β be the roots of the given quadratic equation
Then, α + β = -5/2 and αβ = m/2
Since one of the roots is m, we have
α + β + m = -5/2 + m
Substituting the value of α + β in the above equation, we get
m = -5/2 - m
=> 2m = -5/2
=> m = -5/4
Therefore, the possible values of m are 0 and 2. Hence, option B is the correct answer.

Explanation:
To solve this question, we need to understand the concept of roots of a quadratic equation. When we have a quadratic equation of the form ax² + bx + c = 0, we can find the roots of the equation using the formula (-b ± √(b² - 4ac))/2a. In this question, we are given a quadratic equation and one of the roots is given to be m. We need to find the possible values of m.

Step-by-Step Solution:

1. Write the given quadratic equation as 2x² + 5x + m = 0
2. Use the formula for finding the roots of a quadratic equation to find the sum and product of the roots.
3. Let α and β be the roots of the given quadratic equation. Then, α + β = -5/2 and αβ = m/2.
4. Since one of the roots is m, we have α + β + m = -5/2 + m.
5. Substituting the value of α + β in the above equation, we get m = -5/2 - m.
6. Solving for m, we get 2m = -5/2, which gives us m = -5/4.
7. Therefore, the possible values of m are 0 and 2, which is option B.

Final Answer:
Therefore, the correct answer is option B. The possible values of m are 0 and 2.

2x²+5x-m=0 , *x=m*
apply x in the place of M
2x²+5x-x=0
2x²+4x=0
(2x)(x+2)=0

if 2x=0, then x=0
If ×+2=0 , then x=-2

so , B is the right answer