Let, p(x)=2x^2-5x-(2k+1)--------(1)Also let, α be one root of (1).Then the other root will be 2α.α+2α=-(-5)/2or, 3α=5/2or,α=5/6Again,α + 2α=-(2k+1)/2or, 2α^2=-(2k+1)/2or, -(2k+1)/2=2x(5/6)^2or, -(2k+1)=4x25/36or, -2k-1=25/9or, -2k=25/9+1or, -2k=34/9or, k=-34/9 x 1/2or, k=-17/9 Ans.

Given:
Polynomial: 2x^2 - 5x - (2k + 1)
One zero is twice the other.

To find:
- Both zeroes of the polynomial.
- The value of k.

Solution:

Step 1: Setting up the equation:
Let's assume the two zeroes of the polynomial are a and 2a, where a is a constant.

The equation of the polynomial can be written as:
2x^2 - 5x - (2k + 1) = 0

Step 2: Applying the zero product property:
According to the zero product property, if a polynomial is equal to zero, then each of its factors must be equal to zero.

So, we can set up the following equations:
1. a = 0
2. 2a = 0

Step 3: Solving the equations:
1. a = 0
If a = 0, then the other zero will be 2a = 2(0) = 0. However, in this case, both zeroes will be the same, which contradicts the given condition that one zero is twice the other. Therefore, a = 0 is not a valid solution.

2. 2a = 0
If 2a = 0, then a = 0. This means that one zero is 0, and the other zero is twice this value, which is 2(0) = 0. Again, both zeroes are the same, which contradicts the given condition. Therefore, a = 0 is not a valid solution.

Conclusion:
The polynomial 2x^2 - 5x - (2k + 1) does not have valid zeroes that satisfy the given condition.

Step 4: Solving for k:
Since there are no valid zeroes, we cannot find the value of k. The polynomial does not have a valid solution for any value of k.

Summary:
The polynomial 2x^2 - 5x - (2k + 1) does not have valid zeroes that satisfy the given condition. Therefore, it is not possible to find the value of k.

17/9