If one zero of the quadratic polynomial $39{\mathrm{y}}^2-(2\mathrm{k}+1)\mathrm{y}-22$ is negative of the other, then the value of $\mathrm{k}$ is

If $\mathrm{\alpha }$ and $\mathrm{\beta }$ are zeroes of a quadratic polynomial such that $\mathrm{\alpha }+\mathrm{\beta }=12$ and $\mathrm{\alpha }-\mathrm{\beta }=6$. Then, the family of quadratic polynomials having $\mathrm{\alpha }. \mathrm{\beta }$ as its zeroes is given by

“Note: The option(d) of the question given in the book seems to have errors and the modified option(d) should be as given below.”