The set of values of a such that the equation 2x^2 -2(2a+1)x+a(a-1)=0 has alpha and beta satisfying alpha < a < beta

Answers (1)

Solution:   Let  f(x)=2x^2-2(2a+1)x+a(a-1)

a lies  between the roots of given equation .

\ \ Rightarrow hspace1cm2f(a)< 0Rightarrow f(a)< 0\ \ Rightarrow hspace1cm2a^2-2(2a+1)a+a(a-1)< 0\ \ Rightarrow hspace1cm-a^2-3a< 0Rightarrow a(a+3)> 0\ \ Rightarrow hspace1cmain (infty,-3)cup(0,infty)

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/-
Buy Now
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/-
Buy Now
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/-
Buy Now
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/-
Buy Now
NEET Foundation + Knockout NEET 2025 (Easy Installment)

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

₹ 3999/-
Buy Now
Boost your Preparation for JEE Main with our Foundation Course
 
Exams
Articles
Questions