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Find the values of k for which the...

Find the values of `k` for which the roots are real and equal in the following equations: `k x(x-2)+6=0` (ii) `x^2-4k x+k=0`

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The correct Answer is:
The value of k is 6.
`kx(x-2)+6=0`
`:.kx^(2)-2kx+6=0" "....` (In the standard form)
Here, `a=k,b=-2k,c=6`
`Delta=b^(2)-4ac`
`=(-2k)^(2)-4(k)(6)`
`=4k^(2)-24k`
The roots are real and equal. " "…… (Given)
`:.Delta=0`
`:.4k^(2)-24k=0`
`:.4k(k-6)=0`
`:.4k=0ork-6=0" ":.k=0ork=6`
k=0 is unacceptable, because if k=0, the coefficient of the quadratic term becoms zero. Hence, the equation will not be a quadratic equation.
`:.k=6`
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