Quadratic Equations

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