Category: Algebra

Question Number 19245 by Tinkutara last updated on 07/Aug/17 $$\mathrm{Let}f\left(x\right)\mathrm{be}\mathrm{a}\mathrm{quadratic}\mathrm{polynomial}$$$$\mathrm{with}\mathrm{integer}\mathrm{coefficients}\mathrm{such}\mathrm{that}f\left(0\right)$$$$\mathrm{and}f\left(1\right)\mathrm{are}\mathrm{odd}\mathrm{integers}.\mathrm{Prove}\mathrm{that}$$$$\mathrm{the}\mathrm{equation}f\left(x\right)=0\mathrm{does}\mathrm{not}\mathrm{have}\mathrm{an}$$$$\mathrm{integer}\mathrm{solution}.$$ Commented by RasheedSindhi last updated…

Question Number 19236 by chernoaguero@gmail.com last updated on 07/Aug/17 Answered by ,25>( last updated on 07/Aug/17 $$x=2\mathrm{since}{2}^2+3^2=13.$$ Commented by chernoaguero@gmail.com last…

Question Number 150296 by mathdanisur last updated on 10/Aug/21 Terms of Service Privacy Policy Contact: info@tinkutara.com

Question Number 150289 by mathdanisur last updated on 10/Aug/21 $$\mathrm{If}{}_{\mathbf{n}}{\mathrm{C}}_3-{}_{\mathbf{n}}{\mathrm{C}}_2=14$$$$\mathrm{Find}{}_{\mathbf{n}}{\mathrm{P}}_2=?$$ Answered by Ar Brandon last…

Question Number 19215 by Tinkutara last updated on 07/Aug/17 $$\mathrm{STATEMENT}-1:\mathrm{For}\mathrm{every}\mathrm{natural}$$$$\mathrm{number}n⩾2,\frac{1}{\sqrt{1}}+\frac{1}{\sqrt{2}}+\dots ..\frac{1}{\sqrt{n}}>\sqrt{n}$$$$\mathbf{and}$$$$\mathrm{STATEMENT}-2:\mathrm{For}\mathrm{every}\mathrm{natural}$$$$\mathrm{number}n⩾2,\sqrt{n(n+1)}<n+1$$ Answered by 433 last updated…