Category: Algebra

Question Number 152663 by mr W last updated on 31/Aug/21 $$\mathrm{If}{\mathrm{x}}^3-\mathrm{x}+3=0\mathrm{has}\mathrm{the}\mathrm{roots}\mathrm{a},\mathrm{b}\mathrm{and}\mathrm{c}.$$$$\mathrm{determine}\mathrm{the}\mathrm{monic}\mathrm{polynomial}\mathrm{with}$$$$\mathrm{the}\mathrm{roots}{\mathrm{a}}^5,{\mathrm{b}}^5\mathrm{and}{\mathrm{c}}^5.$$$$\left[Q152396\right]$$ Answered by…

Question Number 152625 by Dandelion last updated on 30/Aug/21 $$x^4+c_3{x}^3+c_2{x}^2+c_{1}x+c_0=0$$$$\mathrm{for}{c}_n\in \mathbb{R}\mathrm{this}\mathrm{can}\mathrm{have}$$$$4\mathrm{unique}\mathrm{zeros}\in \mathbb{R}$$$$\mathrm{2}\:\mathrm{unique}\:\mathrm{zeros}\:+\:\mathrm{1}\:\mathrm{double}\:\mathrm{zero}\:\in\mathbb{R} \…

Question Number 152626 by mathdanisur last updated on 30/Aug/21 $$\mathrm{Solve}\mathrm{for}\mathrm{real}\mathrm{numbers}:$$$$\frac{1}{\mathrm{x}-1}+\frac{2}{\mathrm{x}-2}+\frac{3}{\mathrm{x}-3}+\frac{4}{\mathrm{x}-4}={2\mathrm{x}}^2-5\mathrm{x}-4$$ Answered by MJS_new last updated on 30/Aug/21 $$x=0$$$${x}=\frac{\mathrm{5}}{\mathrm{2}}…

Question Number 21531 by Princejak last updated on 26/Sep/17 $$Factorisetheequationbyfactortheorem$$$$12\hat{x}3+4\hat{x}2-3x-1$$ Commented by Princejak last updated on 26/Sep/17 $${please}\:{answer} \…

Question Number 152596 by liberty last updated on 30/Aug/21 Answered by som(math1967) last updated on 30/Aug/21 $$\mathit{l}\mathit{e}\mathit{t}\frac{3\mathit{x}+\mathit{y}}{4\mathit{y}+3}=\frac{4\mathit{y}+1}{9}=\frac{11}{3\mathit{x}+\mathit{y}}=\mathit{k}$$$$[\because \mathit{a}=\mathit{b}=\mathit{c}]$$$$3\mathit{x}+\mathit{y}=\mathit{k}(4\mathit{y}+3)$$$$4\mathit{y}+1=9\mathit{k}$$$$\mathrm{11}=\boldsymbol{{k}}\left(\mathrm{3}\boldsymbol{{x}}+\boldsymbol{{y}}\right)…