determine the values of k for which the given quadratic equation have equal roots x^2-2(k+1)x+k^2=0.
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On comparing the given equation with general equation, we get
a = 1
b = - 2(k+1)
c = k^2
For equal roots,
Discriminent = 0
=> b^2 - 4ac = 0
=> [ - 2(k + 1)]^2 = 4 (1)(k^2)
=> 4(k+1)^2 = 4k^2
=> 4 ( k^2 + 2k + 1) = 4k^2
=> 4 k^2 + 8k + 4 = 4k^2
=> 8k + 4 = 0
=> 8k = - 4
=> k = - 1/2
a = 1
b = - 2(k+1)
c = k^2
For equal roots,
Discriminent = 0
=> b^2 - 4ac = 0
=> [ - 2(k + 1)]^2 = 4 (1)(k^2)
=> 4(k+1)^2 = 4k^2
=> 4 ( k^2 + 2k + 1) = 4k^2
=> 4 k^2 + 8k + 4 = 4k^2
=> 8k + 4 = 0
=> 8k = - 4
=> k = - 1/2
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