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Question
Find the value of k for which the following equation has equal roots.
x2 + 4kx + (k2 – k + 2) = 0
Solution
For the given equation x2 + 4kx + (k2 – k + 2) = 0
a = 1, b = 4k and c = k2 - k +1
Since the roots are equal,
b2 - 4ac = 0
`=> (4k)^2 - 4xx1xx(k^2 - k + 2) = 0`
`=> 16k^2 - 4k^2 + 4k - `8 = 0`
`=> 12k^2 + 4k - 8 = 0`
`=> 3k^2 + k - 2 = 0`
`=> 3k^2 + 3k - 2k - 2 = 0`
`=> 3k(k+1) - 2(k+1) = 0`
`=> (k+1) (3k - 2) = 0`
`=> k + 1 = 0 or 3k - 2 = 0`
`=> k = -1 or k = 2/3`
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