# The values of p , for which both the roots of equation 4x^2-20px+25p^2+15p-66=0 are less than 2 , belong to

Solution:   Since both the roots are less than 2 , we have

$\\ \\ \Rightarrow \hspace{1cm} D\geq 0\Rightarrow 15p-66\leq0\Rightarrow p\leq\frac{22}{5}\\ \\ \Rightarrow \hspace{1cm}4f(2)> 0\Rightarrow 4(25p^{2}-25p-50)> 0\Rightarrow p^{2}-p-2> 0\\ \\ \Rightarrow \hspace{1cm}-\frac{20}{2\cdot4}< 2\Rightarrow p< \frac{4}{3}$

Taking the intersection of the above three solution , we get    $p\in(\infty,-1)$.

## Most Viewed Questions

### Preparation Products

##### Knockout NEET 2024

Personalized AI Tutor and Adaptive Time Table, Self Study Material, Unlimited Mock Tests and Personalized Analysis Reports, 24x7 Doubt Chat Support,.

₹ 40000/-
##### Knockout NEET 2025

Personalized AI Tutor and Adaptive Time Table, Self Study Material, Unlimited Mock Tests and Personalized Analysis Reports, 24x7 Doubt Chat Support,.

₹ 45000/-
##### NEET Foundation + Knockout NEET 2024

Personalized AI Tutor and Adaptive Time Table, Self Study Material, Unlimited Mock Tests and Personalized Analysis Reports, 24x7 Doubt Chat Support,.

₹ 54999/- ₹ 42499/-
##### NEET Foundation + Knockout NEET 2024 (Easy Installment)

Personalized AI Tutor and Adaptive Time Table, Self Study Material, Unlimited Mock Tests and Personalized Analysis Reports, 24x7 Doubt Chat Support,.

₹ 3999/-