Question

For what value of k are the roots of the quadratic equation `kx(x-2sqrt5)+10=0`real and equal. 

Answer 1

The given equation is 

`kx(x-2sqrt5)+10=0` 

⇒` kx^2-2sqrt5kx+10=0` 

This is of the form `ax^2+bx+c=0` where `a=k, b=-2sqrt5k and c=10` 

The given equation will have real and equal roots if `D=0` 

∴ `20k^2-40k=0` 

⇒`20k(k-2)=0` 

⇒`k=0  or  k-2=0` 

⇒` k=0 or k=2` 

But, for k=0 we get `10=0` which is not true
Hence, 2 is the required value of k.