Multiple choice

Find a quadratic equation each with the given numbers as the sum and product of its zeroes respectively. $2\sqrt 3-1, 3-\sqrt 3$

  1. $x^2-(2\sqrt 5-1)x+(3-\sqrt 3)$
  2. $x^2-(2\sqrt 11-1)x+(3-\sqrt 3)$
  3. $x^2-(2\sqrt 3-1)x+(3-\sqrt 3)$
  4. $x^2-(2\sqrt 7-1)x+(3-\sqrt 3)$
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C Correct answer
Explanation

A quadratic equation is x^2 - (sum of zeroes)x + (product of zeroes). Given sum = 2*sqrt(3) - 1 and product = 3 - sqrt(3), the equation is x^2 - (2*sqrt(3) - 1)x + (3 - sqrt(3)).

AI explanation

The required quadratic equation can be found by substituting the sum and product of its zeros into the standard polynomial form, x^2 - (sum)x + (product). Substituting the given sum of 2*sqrt(3) - 1 and the product of 3 - sqrt(3) into this formula yields x^2 - (2*sqrt(3) - 1)x + (3 - sqrt(3)). This matches the required expression perfectly, establishing it as the correct polynomial.

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