Multiple choice

If A.M. between the roots of a quadratic equation is $8$ and G.M. is $5$, then the equation is?

  1. $x^2+16x-25=0$
  2. $x^2-8x+5=0$
  3. $x^2-16x+25=0$
  4. $x^2-16x-25=0$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

AM = (alpha+beta)/2 = 8 => alpha+beta = 16. GM = sqrt(alpha*beta) = 5 => alpha*beta = 25. Equation: x^2 - (sum)x + (product) = 0 => x^2 - 16x + 25 = 0.

AI explanation

The arithmetic mean is half the sum of the roots, so the sum of the roots is 2 * 8 = 16. The geometric mean is the square root of the product of the roots, so the product is 5^2 = 25. A quadratic equation is x^2 - (sum)x + product = 0, giving x^2 - 16x + 25 = 0.

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