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Question
If the roots of` 5x^2-k+1=0` are real and distinct then
(a)`-2sqrt5<k2<sqrt5` (b)` k>2sqrt5 ` only
(c)` k<-2sqrt5` (d) either `k>2sqrt5 or k<-2sqrt5`
Solution
(d) either `k>2sqrt5 or k<-2sqrt5`
It is given that the roots of the equation `(5x^2-k+1=0)` are real and distinct.
∴ `(b^2-4ac)>0`
⇒`(-k)^2-4xx5xx1>0`
⇒`k^-20>0`
⇒`k^2>20`
⇒`k>sqrt20 or k<-sqrt20`
⇒`k>2sqrt5 or k<-2sqrt5`
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