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Question Number 28174 by ktomboy1992 last updated on 21/Jan/18

if the sum of root 7x+px−q=0 is 7 then p=  ??

$$\mathrm{if}\:\mathrm{the}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{root}\:\mathrm{7x}+\mathrm{px}−\mathrm{q}=\mathrm{0}\:\mathrm{is}\:\mathrm{7}\:\mathrm{then}\:\mathrm{p}= \\ $$$$?? \\ $$

Commented by Rasheed.Sindhi last updated on 21/Jan/18

7x^2 +px−q=0  Sum of the roots=−(p/7)=7        p=−49

$$\mathrm{7x}^{\mathrm{2}} +\mathrm{px}−\mathrm{q}=\mathrm{0} \\ $$$$\mathrm{Sum}\:\mathrm{of}\:\mathrm{the}\:\mathrm{roots}=−\frac{\mathrm{p}}{\mathrm{7}}=\mathrm{7} \\ $$$$\:\:\:\:\:\:\mathrm{p}=−\mathrm{49} \\ $$

Commented by Rasheed.Sindhi last updated on 22/Jan/18

The equation is linear, so it has single  root           7x+px−q=0          x(p+7)=q                x=(q/(p+7))         Sum=(q/(p+7))=7                 7p+49=q                     p=((q−49)/7)

$$\mathrm{The}\:\mathrm{equation}\:\mathrm{is}\:\mathrm{linear},\:\mathrm{so}\:\mathrm{it}\:\mathrm{has}\:\mathrm{single} \\ $$$$\mathrm{root} \\ $$$$\:\:\:\:\:\:\:\:\:\mathrm{7x}+\mathrm{px}−\mathrm{q}=\mathrm{0} \\ $$$$\:\:\:\:\:\:\:\:\mathrm{x}\left(\mathrm{p}+\mathrm{7}\right)=\mathrm{q} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{x}=\frac{\mathrm{q}}{\mathrm{p}+\mathrm{7}} \\ $$$$\:\:\:\:\:\:\:\mathrm{Sum}=\frac{\mathrm{q}}{\mathrm{p}+\mathrm{7}}=\mathrm{7} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{7p}+\mathrm{49}=\mathrm{q} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{p}=\frac{\mathrm{q}−\mathrm{49}}{\mathrm{7}} \\ $$

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