Hello Prithvi! Please see the answer to your question below:
1) The question states that the roots are in a ratio of 2 to 3. This allows us to assume that both are positive.
15/5 = 3. So that tells us that the ratio of 2 to 3 means that one root is 6, and the other is 9.
2) Take the roots and create an equation. If the roots are 6 and 9, that means the factored equation will be:
(x-6)(x-9) . You can check this because x-6=0, so x=6 and x-9=0 so x=9.
3) FOIL (first, outer, inner, last) the two terms. That leaves us with x^2-15x+54, which is the final answer.
