The value of $p$ for which both the roots of the equation $4x^{2}-20px+\left(25p^{2}+15p-66\right)=0$ are less than $2$, lies in the interval

For roots to be less than 2, the vertex -b/2a < 2, f(2) > 0, and discriminant D >= 0. Vertex: 20p/8 = 2.5p < 2 => p < 0.8. f(2) = 4(4) - 20p(2) + 25p^2 + 15p - 66 = 16 - 40p + 25p^2 + 15p - 66 = 25p^2 - 25p - 50 > 0 => p^2 - p - 2 > 0 => (p-2)(p+1) > 0. This holds for p > 2 or p < -1. Combining with p < 0.8, we get p < -1.