Multiple choice

If the sum of the squares of the roots of the equation x2 - 14x + k = 0 is 100, then what is the value of k?

  1. 42

  2. 48

  3. 52

  4. 56
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let the mixture be 1 liter. Selling at 32 with 25% profit means CP = 32/1.25 = 25.6. The cost of pure lemonade is 40. Using alligation: (40-25.6) / (25.6-0) = 14.4 / 25.6 = 144/256 = 9/16.

AI explanation

Let the roots of the quadratic equation x2 - 14x + k = 0 be alpha and beta. Using the sum and product of roots formulas, we have alpha + beta = 14 and alpha beta = k. The sum of the squares of the roots is given as 100, so we use the identity alpha2 + beta2 = (alpha + beta)2 - 2 alpha beta. Substituting the known values gives 100 = (14)2 - 2k, which simplifies to 100 = 196 - 2k. Solving for k yields 2k = 96, so k = 48.

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