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Question
Find the value(s) of k so that the quadratic equation x2 − 4kx + k = 0 has equal roots.
Solution
Given equation is x2 − 4kx + k = 0
For the given equation to have equal roots, D = 0.
`rArr b^2-4ac=0 `
`rArr (-4k)^2-4(1)(k)=0`
`rArr 16k^2-4k=0`
`rArr 4k(4k-1)=0`
`rArr4k=0`or `k=1/4`
Hence, for k = 0 or `1/4`, the given equation will have equal roots.
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