If a non-zero number *N*, diminished by 4 times its reciprocal, equals a given real constant *R*, then in terms of *R*, the sum of all such possible values of *N* is:

- 1/
*R* *R*- 4
- 1/4
- –
*R*

Since N – |
4 | = R → N – |
4 | – R = 0 → N^{2} − 4 − RN = 0 → N^{2} − RN − 4 = 0. |

N |
N |

So we have a nice quadratic in *N*, and

N = |
R ± √R^{2} + 16 |
. |

2 |

So

N = |
R + √ |
or | N = |
R− √ |
. |

2 | 2 |

The sum of the *N*‘s is

R + √ |
+ | R − √ |
= | R |
+ | √ | + | R |
− | √ | = | 2R |
= R. |

2 | 2 | 2 | 2 | 2 | 2 | 2 |

The answer is (b).