2024 · Q7
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?
Elementary MathematicsAlgebra
- AThere are infinitely many such equations having different roots.
- BThere is only one such equation which is x² + 2x - 100 = 0.
- CThere is only one such equation which is x² - 2x - 100 = 0.
- DThere is no such equation.
Explanation
A monic quadratic with roots 1 ± √101 is x² − (sum)x + (product) = x² − 2x − 100 = 0, since the sum is 2 and the product is 1 − 101 = −100. Being monic, this equation is unique. Hence the answer is option (c).