How many quadratic equations have a given sum and product of roots

1. A.
   Zero
2. B.
   One
3. C.
   Two
4. D.
   Infinitely many

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1. A.
   There are infinitely many such equations having different roots.
2. B.
   There is only one such equation which is $x^2 + 2x - 100 = 0$.
3. C.
   There is only one such equation which is $x^2 - 2x - 100 = 0$.
4. D.
   There is no such equation.

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