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Question Number 175061 by daus last updated on 17/Aug/22

Commented by Rasheed.Sindhi last updated on 17/Aug/22

$$\left(\mathrm{a}\right)150$$

Answered by cortano1 last updated on 18/Aug/22

$$q\left(x\right)=p\left(x\right)(x^5-2x+2)$$$$\left(a\right)\Rightarrow \{\begin{array}{l}p\left(2\right)-5=0\Rightarrow p\left(2\right)=5\\ q\left(2\right)=p\left(2\right)(32-4+2)\\ q\left(2\right)=5\left(30\right)=150\end{array}$$$$\left(b\right)p\left(1\right)-5=0\Rightarrow p\left(1\right)=5$$$$1+a+b=5\Rightarrow a+b=4$$$$p\left(x\right)-5=x^2+ax+b-5$$$$x^2+ax+b-5=(x-1)(x-2)=x^2-3x+2$$$$a=-3;b=5+2=7$$$$$$

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