2021 · Q10
The sum and the product of the roots of a quadratic equation are 7 and 12 respectively. If the bigger root is halved and the smaller root is doubled, then what is the resulting quadratic equation ?
Elementary MathematicsAlgebra
- Ax² − 6x + 12 = 0
- Bx² − 8x + 12 = 0
- Cx² + 8x + 12 = 0
- Dx² − 10x + 12 = 0
Explanation
Roots with sum 7 and product 12 satisfy t² − 7t + 12 = 0, i.e. t = 3 and t = 4. Halving the bigger root gives 2 and doubling the smaller gives 6. The equation with roots 2 and 6 is x² − (2+6)x + 2·6 = x² − 8x + 12 = 0. This is option (b).