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Question Number 32794 by Rio Mike last updated on 02/Apr/18
given that the point (t^� ,0) lies on the  curve y=2x^2 −x. find the value of t.
$${given}\:{that}\:{the}\:{point}\:\left(\bar {{t}},\mathrm{0}\right)\:{lies}\:{on}\:{the} \\ $$$${curve}\:{y}=\mathrm{2}{x}^{\mathrm{2}} −{x}.\:{find}\:{the}\:{value}\:{of}\:{t}. \\ $$
Answered by Joel578 last updated on 02/Apr/18
y = 2x^2  − x  0 = 2t^2  − t  t(2t − 1) = 0  t = 0    ∨    t = (1/2)
$${y}\:=\:\mathrm{2}{x}^{\mathrm{2}} \:−\:{x} \\ $$$$\mathrm{0}\:=\:\mathrm{2}{t}^{\mathrm{2}} \:−\:{t} \\ $$$${t}\left(\mathrm{2}{t}\:−\:\mathrm{1}\right)\:=\:\mathrm{0} \\ $$$${t}\:=\:\mathrm{0}\:\:\:\:\vee\:\:\:\:{t}\:=\:\frac{\mathrm{1}}{\mathrm{2}} \\ $$

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