Question

If $\alpha$ and $\beta$ are zeroes of polynomial$6x^2-5x+kand\alpha -\beta =\frac{1}{6}$ find k

Answer 1

$6x^2-5x+k\alpha +\beta =\frac{5}{6}\alpha -\beta =\frac{1}{6}$
Adding these two equations,
$2\alpha =\frac{5}{6}+\frac{1}{6}=1\to \alpha =\frac{1}{2}\to \beta =\frac{5}{6}-\frac{1}{2}=\frac{2}{6}\alpha x\beta =\frac{k}{6}=\frac{1}{2}\times \frac{2}{6}=\frac{1}{6}\to k=1$