Find the value of k such that the quadratic polynomials x2-(k+6)x+2(2k+1) as sum of the zeroes as the half of their product

  k = 5

Step-by-step explanation:

The sum of the zeros is the opposite of the coefficient of x, so is (k+6).

The product of zeros is the constant term, 2(2k+1), so half their product is (2k+1).

The problem statement asks us to find k so that these values are the same:

  k +6 = 2k +1

  5 = k . . . . . . . . subtract k+1

The value of k is 5.

The zeros are 5.5±√8.25. Their sum is 11; their product is 22.

207/8 is the right