Question and Answers Forum

All Questions      Topic List

Algebra Questions

Previous in All Question      Next in All Question      

Previous in Algebra      Next in Algebra      

Question Number 105345 by bemath last updated on 28/Jul/20

If the point ((√2) ,p) and (−(√2),q)  lie on the graph y=x^3 +ax^2 +bx+c  and q−p = 3 , then what the  value of b ?

$${If}\:{the}\:{point}\:\left(\sqrt{\mathrm{2}}\:,{p}\right)\:{and}\:\left(−\sqrt{\mathrm{2}},{q}\right) \\ $$$${lie}\:{on}\:{the}\:{graph}\:{y}={x}^{\mathrm{3}} +{ax}^{\mathrm{2}} +{bx}+{c} \\ $$$${and}\:{q}−{p}\:=\:\mathrm{3}\:,\:{then}\:{what}\:{the} \\ $$$${value}\:{of}\:{b}\:?\: \\ $$

Answered by ajfour last updated on 28/Jul/20

p=2(√2)+2a+b(√2)+c  q=−2(√2)+2a−b(√2)+c  subtracting  −3=2(√2)(b+2)   ⇒  b=−2−((3(√2))/4)   b = −[2+(3/4)((√2))] .

$${p}=\mathrm{2}\sqrt{\mathrm{2}}+\mathrm{2}{a}+{b}\sqrt{\mathrm{2}}+{c} \\ $$$${q}=−\mathrm{2}\sqrt{\mathrm{2}}+\mathrm{2}{a}−{b}\sqrt{\mathrm{2}}+{c} \\ $$$${subtracting} \\ $$$$−\mathrm{3}=\mathrm{2}\sqrt{\mathrm{2}}\left({b}+\mathrm{2}\right)\:\:\:\Rightarrow\:\:{b}=−\mathrm{2}−\frac{\mathrm{3}\sqrt{\mathrm{2}}}{\mathrm{4}} \\ $$$$\:{b}\:=\:−\left[\mathrm{2}+\frac{\mathrm{3}}{\mathrm{4}}\left(\sqrt{\mathrm{2}}\right)\right]\:. \\ $$

Commented by bemath last updated on 28/Jul/20

cooll...

$${cooll}... \\ $$

Terms of Service

Privacy Policy

Contact: info@tinkutara.com