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?
- A. x^{2}-6x+12=0
- B. x^{2}-8x+12=0 ✓
- C. x^{2}+8x+12=0
- D. x^{2}-10x+12=0
Correct Answer: B. x^{2}-8x+12=0
Explanation
The roots of the original equation (x^2 - 7x + 12 = 0) are 4 and 3. The new roots are 4/2 = 2 and 3 \times 2 = 6. The new equation is x^2 - (2+6)x + (2 \times 6) = 0 \implies x^2 - 8x + 12 = 0.
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