Multiple choice

If the quadratic equation ax² + bx + c = 0 has roots in the ratio 3 : 5, and the sum of the roots is -16, find the values of a, b, and c.

  1. a = 2, b = 16, c = -24

  2. a = 5, b = 16, c = 45

  3. a = 3, b = -16, c = 45

  4. None of the above
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D Correct answer
AI explanation

If the roots are in the ratio 3 to 5 and their sum is negative 16, the roots are negative 6 and negative 10. The product of these roots is 60, so any correct equation must have the ratio c to a equal to 60. Checking the provided options, the ratio for the first is negative 12, for the second is 9, and for the third is 15. Because none of the options match the required product ratio, none of the above are correct.

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