Multiple choice

Find the quadratic polynomial with zeroes $3+\sqrt{2}$ & $3-\sqrt{2}$.

  1. $x^2-6x-7$
  2. $x^2-6x+6$
  3. $x^2+6x+7$
  4. $x^2-6x+7$
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D Correct answer
Explanation

Sum of zeroes = 3+sqrt(2) + 3-sqrt(2) = 6. Product = (3+sqrt(2))(3-sqrt(2)) = 9 - 2 = 7. Polynomial = x^2 - (sum)x + product = x^2 - 6x + 7.

AI explanation

Use the sum and product of zeroes formulas to construct the polynomial, where the sum equals 6 and the product equals 7. The required quadratic polynomial is x^2 - (sum)x + (product). Substituting the values gives x^2 - 6x + 7.

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