If the sum and product of the roots of a quadratic equation are 2 and −100 respectively, then which one of the following is correct ?

For a quadratic ax² + bx + c = 0, sum of roots = −b/a and product = c/a. The equation x² − 2x − 100 = 0 has these properties, but so does 2x² − 4x − 200 = 0, 3x² − 6x − 300 = 0, etc. All these have the same roots though. However, the question asks about equations (not roots). Since multiplying by any constant gives a 'different' equation but with the same roots. If we require monic quadratic (a=1), there is exactly one: x² − 2x − 100 = 0. The phrase 'infinitely many such equations having different roots' is incorrect because the roots are fixed by sum and product. Hence the answer is (c): There is only one such equation x² − 2x − 100 = 0.