Form a quadratic polynomial with modified zeroes

For $25p^2 - 15p + 2$: $\alpha + \beta = \frac{15}{25} = \frac{3}{5}, \quad \alpha\beta = \frac{2}{25}$ Let the new zeroes be $S_1 = \frac{1}{3\alpha}$ and $S_2 = \frac{1}{3\beta}$. Sum of new zeroes $S = S_1 + S_2 = \frac{1}{3}\left(\frac{\alpha + \beta}{\alpha\beta}\right) = \frac{1}{3}\left(\frac{3/5}{2/25}\right) = \frac{1}{3}\left(\frac{15}{2}\right) = \frac{5}{2}$. Product of new zeroes $P = S_1 S_2 = \frac{1}{9\alpha\beta} = \frac{1}{9(2/25)} = \frac{25}{18}$. Required polynomial is $k\left(x^2 - Sx + P\right) = k\left(x^2 - \frac{5}{2}x + \frac{25}{18}\right)$. Taking $k = 18$, polynomial is $18x^2 - 45x + 25$.