Multiple choice general knowledge math & puzzles

The sum of the reciprocals of the roots of the equation ax^2+bx+c is 22. The product of the roots of the equation cx^2+bx+a is 11. What is the difference of the roots of the equation ax^2+bx+c

  1. (20/11)^0.5

  2. (40/11)^0.5

  3. (30/11)^0.5

  4. (50/11)^0.5
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B Correct answer
Explanation

For ax²+bx+c: sum of roots = -b/a, product = c/a. Sum of reciprocals = (sum)/(product) = (-b/a)/(c/a) = -b/c = 22. For cx²+bx+a: product = a/c = 11, so a = 11c. From -b/c = 22, b = -22c. In ax²+bx+c: difference of roots = √[(sum)² - 4(product)] = √[(-b/a)² - 4(c/a)] = √[(22c/11c)² - 4(c/11c)] = √[(2)² - 4/11] = √[4 - 4/11] = √(40/11).

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