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Question
Find the values of k for which the given quadratic equation has real and distinct root:
`5x^2-kx+1=0`
Solution
The given equation is` 5x^2-kx+1=0`
∴` D=(-k)^2-4xx5xx1=k^2-20`
The given equation has real and distinct roots if `D >0`
∴` k^2-20>0`
⇒ `k^2-(2sqrt5)^2>0`
⇒ `(k-2sqrt5) (k+2sqrt5)>0`
⇒`k<-2sqrt5 or k>2sqrt5`
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