The-quadratic-equations-x-2-6x-a-0-and-x-2-cx-6-0-have-one-root-in-common-The-other-roots-of-the-first-and-second-equations-are-integers-in-the-ratio-4-3-Then-find-the-common-root- Tinku Tara June 4, 2023 Algebra 0 Comments FacebookTweetPin Question Number 20118 by Tinkutara last updated on 22/Aug/17 Thequadraticequationsx2−6x+a=0andx2−cx+6=0haveonerootincommon.Theotherrootsofthefirstandsecondequationsareintegersintheratio4:3.Then,findthecommonroot. Answered by ajfour last updated on 22/Aug/17 Letthecommonrootbeααβ=a,α+β=6,αγ=6,α+γ=c⇒β−γ=6−cβγ=a6=43⇒a=8α+β=6;αβ=8,⇒α=2,4Acheck:ifα=2,thenβ=4,andγ=34β=3ifα=4,thenβ=2,andγ=34β=32;notaninteger.Henceα=2.c=α+γ=2+3=5. Commented by Tinkutara last updated on 22/Aug/17 ThankyouverymuchSir! Terms of Service Privacy Policy Contact: info@tinkutara.com FacebookTweetPin Post navigation Previous Previous post: Question-151191Next Next post: In-ABC-the-following-relationship-holds-golden-ratio-sinA-sinB-sinC-lt-1-1-2- Leave a Reply Cancel replyYour email address will not be published. Required fields are marked *Comment * Name * Save my name, email, and website in this browser for the next time I comment.