Find the values of `k` for which the given quadratic equation has real and distinct roots: (i) `k x^2+2x+1=0` (ii) `k x^2+6x+1=0` (iii) `x^2-k x+9=0`

Explanation

`Rightarrow` The given quadratic equation is `x^{2}-k x+9=0, `comparing it with` a x^{2}+b x+ c=0`

We have , a=1 b=-k, c=9

`Rightarrow `It is given that roots are real and distinct.

So,` b^{2}-4 a c>0`

`Rightarrow(-{k})^{2}-4(1)(9)>0`

`Rightarrow {k}^{2}-36>0`

`Rightarrow {k}^{2}>36`

`Rightarrow {k}>6 or {k}<-6`

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