Multiple choice

If the arithmetic mean between the roots of a quadratic equation is 8 and the geometric mean between them is 5, the equation is:

  1. x2 - 16x - 25 = 0

  2. x2 - 16x + 25 = 0

  3. x2 + 16x + 25 = 0

  4. None of these
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B Correct answer
Explanation

For roots a and b, (a+b)/2 = 8 implies a+b = 16. sqrt(ab) = 5 implies ab = 25. The quadratic equation is x^2 - (sum)x + (product) = 0, which is x^2 - 16x + 25 = 0.

AI explanation

Let the roots be a and b, so the arithmetic mean gives (a + b) / 2 = 8, meaning the sum of the roots is 16. The geometric mean gives the square root of ab = 5, meaning the product of the roots is 25. Using the standard form of a quadratic equation x^2 - (sum)x + (product) = 0, we substitute the values to get x^2 - 16x + 25 = 0.

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