Multiple choice

Find a quadratic polynomial each with the given numbers as the zeroes of the polynomial. $2\sqrt 3, -2\sqrt 3$

  1. $x^2+12$
  2. $x^2+2x-12$
  3. $x^2-2x+12$
  4. $x^2-12$
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D Correct answer
Explanation

A quadratic polynomial with zeroes a and b is x^2 - (a+b)x + ab. Here, a+b = 0 and ab = (2*sqrt(3)) * (-2*sqrt(3)) = -12. The polynomial is x^2 - 12.

AI explanation

To find a quadratic polynomial with zeroes at 2*sqrt(3) and -2*sqrt(3), we use the sum and product of roots formulas. The sum of the zeroes is 2*sqrt(3) - 2*sqrt(3) = 0, and the product is (2*sqrt(3))(-2*sqrt(3)) = -12. The polynomial is formed as x^2 - (sum)x + product, resulting in x^2 - 12.

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