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  4. The value of k for which the roots of the equation x2+2(k+1)x+k2=0 are equal to

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Q. The value of $k$ for which the roots of the equation $ {{x}^{2}}+2(k+1)x+{{k}^{2}}=0 $ are equal to

Rajasthan PETRajasthan PET 2010

Solution:

Since roots of the equation
$ {{x}^{2}}+2(k+1)x+{{k}^{2}}=0 $
are equal.
$ \therefore $ $ {{B}^{2}}=4AC $
$ \Rightarrow $ $ 4{{(k+1)}^{2}}=4{{k}^{2}} $
$ \Rightarrow $ $ 4{{k}^{2}}+4+8k=4{{k}^{2}} $
$ \Rightarrow $ $ k=-\frac{1}{2} $