The complete set of values of a for which the roots of the equation \( x^{2}-2|a+1| x+1=0 \) are...

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The complete set of values of a for which the roots of the equation \( x^{2}-2|a+1| x+1=0 \) are real is given by:
(a) \( (-\infty,-2] \cup[0, \infty) \)
(b) \( (-\infty,-1] \cup[0, \infty) \)
(c) \( (-\infty,-1] \cup[1, \infty) \)
(d) \( (-\infty,-2] \cup[1, \infty) \)
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