Please-can-someone-help-with-a-simplier-method-of-solving-this-question-Q1-Given-that-the-expression-x-3-x-2-4x-5-and-x-3-3x-7-leave-same-remainder-when-divided-by-x-a-find-the-possi

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Question Number 33455 by Rio Mike last updated on 16/Apr/18

$$Pleasecansomeonehelpwitha$$$$simpliermethodofsolvingthisquestion$$$$Q1;$$$$Giventhattheexpression{x}^3+x^2-4x+5$$$$and{x}^3+3x-7leavesameremainder$$$$whendividedby(x-a)findthepossible$$$$valuesofa$$

Commented by prof Abdo imad last updated on 17/Apr/18

$$x^3+x^2-4x+5=(x-a)Q\left(x\right)+r\left(x\right)$$$$x^3+3x-7=(x-a)V\left(x\right)+r\left(x\right)\Rightarrow$$$$r\left(a\right)=a^3+a^2-4a+5=a^3+3a-7\Rightarrow$$$$a^2-4a+5-3a+7=0\Rightarrow a^2-7a+12=0$$$$\mathrm{\Delta }=49-48=1\Rightarrow a_1=\frac{7+1}{2}=4$$$$a_2=\frac{7-1}{2}=3.$$

Commented by tanmay.chaudhury50@gmail.com last updated on 17/Apr/18

$$a^3+a^{2\stackrel{}{}}-4a+5=a^3+3a-7$$$$a^2-7a+12=0$$$$(a-3)(a-4)=0$$$$a=3ora=4$$

Answered by ajfour last updated on 16/Apr/18

$$letremainder=R$$$$\Rightarrow a^3+a^2-4a+5=a^3+3a-7=R$$$$\Rightarrow a^2-7a+12=0$$$$or(a-3)(a-4)=0$$$$\Rightarrow a=3,4.$$

Commented by Rio Mike last updated on 16/Apr/18

$$thanksverysimplenow$$

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