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