Question

Find the values of k for which the given quadratic equation has real and distinct root:  

`5x^2-kx+1=0` 

 

 

Answer 1

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`