The roots of the quadratic equation x2−35x+c=0 are given to be in the ratio 2:3. Let's assume the roots are 2α and 3α. The sum of the roots is given by the equation: 2α+3α=5α=35 Solving for α, we get: α=7 The product of the roots can be expressed as: (2α)(3α)=6α2=c Substituting the value of α, we find: c=6×72=6×49 Given that c=6K, we equate to find K : 6×49=6K K=49