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Question Number 101590 by student work last updated on 03/Jul/20

p(2x+5)=(2x^2 +3x−1)Q(x+1) if Q(−1)=3 then p(1)=?

$$\mathrm{p}\left(\mathrm{2x}+\mathrm{5}\right)=\left(\mathrm{2x}^{\mathrm{2}} +\mathrm{3x}−\mathrm{1}\right)\mathrm{Q}\left(\mathrm{x}+\mathrm{1}\right) \\ $$$$\mathrm{if}\:\mathrm{Q}\left(−\mathrm{1}\right)=\mathrm{3}\:\:\:\:\:\mathrm{then}\:\mathrm{p}\left(\mathrm{1}\right)=? \\ $$

Commented by Tinku Tara last updated on 03/Jul/20

You couldnt simple have doubt on this question when you are working on ∫x^x ?

$$\mathrm{You}\:\mathrm{couldnt}\:\mathrm{simple}\:\mathrm{have}\:\mathrm{doubt} \\ $$$$\mathrm{on}\:\mathrm{this}\:\mathrm{question}\:\mathrm{when}\:\mathrm{you}\:\mathrm{are}\:\mathrm{working} \\ $$$$\mathrm{on}\:\int{x}^{{x}} ? \\ $$

Answered by prakash jain last updated on 03/Jul/20

put x=−2 p(1)=(8−6−1)Q(−1)=3

$$\mathrm{put}\:{x}=−\mathrm{2} \\ $$$${p}\left(\mathrm{1}\right)=\left(\mathrm{8}−\mathrm{6}−\mathrm{1}\right){Q}\left(−\mathrm{1}\right)=\mathrm{3} \\ $$

Commented by student work last updated on 03/Jul/20

help me to write the all practice

$$\mathrm{help}\:\mathrm{me}\:\mathrm{to}\:\mathrm{write}\:\mathrm{the}\:\mathrm{all}\:\mathrm{practice} \\ $$

Answered by bemath last updated on 03/Jul/20

let x+1 = z ⇒x=z−1 P(2z+3)=(2(z−1)^2 +3(z−1)−1)Q(z) take z=−1 then P(−2+3)=(2(−2)^2 +3(−2)−1)Q(−1) P(1)=(8−6−1)(3) P(1)= 1×3 = 3 ★

$$\mathrm{let}\:\mathrm{x}+\mathrm{1}\:=\:\mathrm{z}\:\Rightarrow\mathrm{x}=\mathrm{z}−\mathrm{1} \\ $$$$\mathrm{P}\left(\mathrm{2z}+\mathrm{3}\right)=\left(\mathrm{2}\left(\mathrm{z}−\mathrm{1}\right)^{\mathrm{2}} +\mathrm{3}\left(\mathrm{z}−\mathrm{1}\right)−\mathrm{1}\right)\mathrm{Q}\left(\mathrm{z}\right) \\ $$$$\mathrm{take}\:\mathrm{z}=−\mathrm{1} \\ $$$$\mathrm{then}\:\mathrm{P}\left(−\mathrm{2}+\mathrm{3}\right)=\left(\mathrm{2}\left(−\mathrm{2}\right)^{\mathrm{2}} +\mathrm{3}\left(−\mathrm{2}\right)−\mathrm{1}\right)\mathrm{Q}\left(−\mathrm{1}\right) \\ $$$$\mathrm{P}\left(\mathrm{1}\right)=\left(\mathrm{8}−\mathrm{6}−\mathrm{1}\right)\left(\mathrm{3}\right) \\ $$$$\mathrm{P}\left(\mathrm{1}\right)=\:\mathrm{1}×\mathrm{3}\:=\:\mathrm{3}\:\bigstar \\ $$

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