Question-213641 Tinku Tara November 12, 2024 Algebra 0 Comments FacebookTweetPin Question Number 213641 by Abdullahrussell last updated on 12/Nov/24 Answered by Ghisom last updated on 03/Dec/24 αk∈Zp(x)=∑nk=3αkxkx∈Z⇒p(x)∈Zwe′llneedthislater:2∣pq⇒2∣p∨2∣q2∤pq⇒2∤p∧2∤q⇒2∣αkxk⇒2∣αk(x+2)k2∤αkxk⇒2∤αk(x+2)k⇒(2∣p(x)∧2∣p(x+2))∨(2∤p(x)∧2∤p(x+2))★f(x)=p(x)+ax2+bx+cinsertingf(1)=2∧f(2)=3∧f(3)=5andsolvingfora,b,cwegeta=12−p(1)2+p(2)−p(3)2b=−12+5p(1)2−4p(2)+3p(3)2c=2−3p(1)+3p(2)−p(3)⇒c∈Za∈Z⇒12−p(1)2−p(3)2=M∈Zb∈Z⇒−12+5p(1)2+3p(3)2=N∈Z⇒p(1)=3M+N−1p(3)=−5M−N+2allcombinationsofMandNbeingoddorevenyield2∣p(1)⇔2∤p(3)∧2∤p(1)⇔2∣p(3)butp(3)=p(1+2)⇒contradictionto★ Terms of Service Privacy Policy Contact: info@tinkutara.com FacebookTweetPin Post navigation Previous Previous post: Find-the-maximum-value-of-3sin-2-x-8cosx-5-Next Next post: Question-213656 Leave a Reply Cancel replyYour email address will not be published.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.