If the roots of the equation $x^2-px+54=0$ are in the ratio $2:3$, then the value of $p$ is

Let the roots of the quadratic equation $x^2-px+54=0$ be $\alpha$ and $\beta$.Given that the ratio of roots is $\alpha :\beta =2:3$, we can define the roots as:
$$\alpha =2k\text{and}\beta =3k$$
From the standard relationships of a quadratic equation:Product of roots:
$$\alpha \times \beta =\frac{c}{a}⟹(2k)\times (3k)=54$$
$$6k^2=54$$
$$k^2=9⟹k=\pm 3$$
Sum of roots:
$$\alpha +\beta =-\frac{(-p)}{1}=p$$
$$2k+3k=p⟹5k=p$$
Case 1: If $k=3$, then $p=5(3)=15$.Case 2: If $k=-3$, then $p=5(-3)=-15$.Looking at the options provided, $15$ is present in option D.