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For what value of k, are the roots of the quadratic equation kx (x-2) +6 = 0equal ?

Answer» The given equation is `kx^(2)-2kx+6=0.`
This is of the form `ax^(2)+bx+c=0,` where a=k, b=-2k and c=6.
`:." "D=(b^(2)-4ac)=(4k^(2)-4xxkxx6)=(4k^(2)-24k).`
For equal roots, we must have
`D=0implies4k^(2)-24k=0implies4k(k-6)=0impliesk=0" or "k=6.`
Now, k=0, we get 6=0, which is absurd.
`:." "kne0` andm hance k=6.


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