If $$x^2 + kx + k = 0$$ has repeated roots, then the value of $$k$$ will satisfy:
For repeated root,
Discriminate Must be = 0
Thus, $$D = b^2 - 4ac$$
Here, b = k , a = 1 & c = k
=> $$k^2 - 4\times k$$ = 0
=> k(k-4) = 0
=> k = 4 or k = 0
Thus, value of k is Natural number
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