Question and Answers Forum

All Questions      Topic List

UNKNOWN Questions

Previous in All Question      Next in All Question      

Previous in UNKNOWN      Next in UNKNOWN      

Question Number 63539 by REHEMAABDDUL last updated on 05/Jul/19

The minimum value of 2x^2 −3x+2 is ___.

$$\mathrm{The}\:\mathrm{minimum}\:\mathrm{value}\:\mathrm{of}\:\mathrm{2}{x}^{\mathrm{2}} −\mathrm{3}{x}+\mathrm{2}\:\mathrm{is}\:\_\_\_. \\ $$

Commented by Prithwish sen last updated on 05/Jul/19

= 2(x−(3/4))^2 +(7/8)  ∵ 2(x−(3/4))^2 ≥0  ∴ the minimum value = (7/8)

$$=\:\mathrm{2}\left(\mathrm{x}−\frac{\mathrm{3}}{\mathrm{4}}\right)^{\mathrm{2}} +\frac{\mathrm{7}}{\mathrm{8}} \\ $$$$\because\:\mathrm{2}\left(\mathrm{x}−\frac{\mathrm{3}}{\mathrm{4}}\right)^{\mathrm{2}} \geqslant\mathrm{0} \\ $$$$\therefore\:\mathrm{the}\:\mathrm{minimum}\:\mathrm{value}\:=\:\frac{\mathrm{7}}{\mathrm{8}} \\ $$

Commented by meme last updated on 05/Jul/19

a=2>0  the minimum is x=(3/4)

$${a}=\mathrm{2}>\mathrm{0} \\ $$$${the}\:{minimum}\:{is}\:{x}=\frac{\mathrm{3}}{\mathrm{4}} \\ $$

Answered by Rio Michael last updated on 05/Jul/19

 min value = ((4ac−b^2 )/(4a))    min val= ((4(2)(2)−(−3)^2 )/(4(2)))                       = (7/8)

$$\:{min}\:{value}\:=\:\frac{\mathrm{4}{ac}−{b}^{\mathrm{2}} }{\mathrm{4}{a}} \\ $$$$\:\:{min}\:{val}=\:\frac{\mathrm{4}\left(\mathrm{2}\right)\left(\mathrm{2}\right)−\left(−\mathrm{3}\right)^{\mathrm{2}} }{\mathrm{4}\left(\mathrm{2}\right)} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:=\:\frac{\mathrm{7}}{\mathrm{8}} \\ $$

Terms of Service

Privacy Policy

Contact: info@tinkutara.com