Multiple choice

If sum of the squares of zeroes of the quadratic polynomial f(x) = x2 - 8x + k is 40, the value of k is

  1. 10

  2. 12

  3. 14

  4. 16
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B Correct answer
Explanation

For f(x) = x^2 - 8x + k, roots alpha and beta satisfy alpha+beta = 8 and alpha*beta = k. alpha^2 + beta^2 = (alpha+beta)^2 - 2*alpha*beta = 40. 8^2 - 2k = 40 => 64 - 2k = 40 => 2k = 24 => k = 12.

AI explanation

For the polynomial x squared minus 8x plus k, the sum of the zeros is 8 and the product is k. The sum of the squares of the zeros is the square of the sum minus twice the product. Substituting the known values gives 8 squared minus 2 times k equals 40, so 64 minus 2k equals 40. Solving this gives 2k equals 24, meaning k equals 12.

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