Search for: If α,β are the roots of the equation x2−3x+5=0 and γ,δ are the roots of the equation x2+5x−3=0, then the equation whose roots are αγ+βδ and αδ+βγ isIf α,β are the roots of the equation x2−3x+5=0 and γ,δ are the roots of the equation x2+5x−3=0, then the equation whose roots are αγ+βδ and αδ+βγ isAx2−15x−158=0Bx2+15x−158=0Cx2−15x+158=0Dx2+15x+158=0 Register to Get Free Mock Test and Study Material +91 Verify OTP Code (required) I agree to the terms and conditions and privacy policy. Solution:∵α+β=3,αβ=5,γ+δ=(−5),γδ=(−3)Sum of roots =(αγ+βδ)+(αδ+βγ) =(α+β)(γ+δ)=3×(−5)=(−15)Product of roots =(αγ+βδ)(αδ+βγ) =α2γδ+αβγ2+βαδ2+β2γδ =γδ(α2+β2)+αβ(γ2+δ2) =−3(α2+β2)+5(γ2+δ2) =−3[(α+β)2−2αβ]+5[(γ+δ)2−2γδ] =−3[9−10]+5[25+6]=158Required equation is x2+15x+158=0Post navigationPrevious: If f:R→R, g :R→R be two functions given by f(x)=2x-3, g(x)=x3+5. Then,fog-1(x) is equal to Next: Given sum of the first n terns of an AP is 2n + 3 n2. Another AP is formed with the same first term and double of the common difference, the sum of n terms of the new AP isRelated content NEET 2024 JEE Advanced 2023 NEET Rank Assurance Program | NEET Crash Course 2023 JEE Main 2023 Question Papers with Solutions JEE Main 2024 Syllabus Best Books for JEE Main 2024 JEE Advanced 2024: Exam date, Syllabus, Eligibility Criteria JEE Main 2024: Exam dates, Syllabus, Eligibility Criteria JEE 2024: Exam Date, Syllabus, Eligibility Criteria NCERT Solutions For Class 6 Maths Data Handling Exercise 9.3