Multiple choice

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?

  1. x2 - 6x + 12 = 0

  2. x2 - 8x + 12 = 0

  3. x2 + 8x + 12 = 0

  4. x2 - 10x + 12 = 0
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B Correct answer
Explanation

Roots a, b satisfy a+b=7, ab=12. Roots are 3 and 4. Bigger root halved = 4/2 = 2. Smaller root doubled = 3*2 = 6. New roots 2 and 6. New equation: x^2 - (2+6)x + (2*6) = 0, which is x^2 - 8x + 12 = 0.

AI explanation

The roots of the quadratic equation are the factors of 12 that sum to 7, which are 4 and 3. Halving the bigger root gives 2 and doubling the smaller root gives 6, making the sum of the new roots 8 and the product 12. The required quadratic equation is x2 - 8x + 12 = 0.

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