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Given-that-the-curve-y-2x-2-19x-18-does-not-intersect-the-line-y-x-k-find-the-largest-integer-of-k-

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Question Number 120705 by ZiYangLee last updated on 02/Nov/20
Given that the curve y=2x^2 −19x+18 does not intersect the line y=x+k, find the largest integer of k.
Giventhatthecurvey=2x2−19x+18doesnotintersecttheliney=x+k,findthelargestintegerofk.
Commented by john santu last updated on 02/Nov/20
⇒2x^2 −19x+18=x+k ⇒2x^2 −20x+18−k=0 take discriminant < 0 ⇒400−4.2.(18−k)<0 ⇒256+8k<0 ⇒32+k<0 , k<−32 so we get k=−33 the largest integer of k
⇒2x2−19x+18=x+k⇒2x2−20x+18−k=0takediscriminant<0⇒400−4.2.(18−k)<0⇒256+8k<0⇒32+k<0,k<−32sowegetk=−33thelargestintegerofk

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