Multiple choice

Form the quadratic equation with rational coefficient, if its one of the root is$\sqrt5\,-\,\sqrt3$, then the equation is

  1. $x^2\,\pm\,6x\,+\,6\,=\,0$
  2. $x^2\,\pm\,7x\,+\,6\,=\,0$
  3. $x^2\,\pm\,7x\,+\,16\,=\,0$

  4. none of the above
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D Correct answer
AI explanation

For a rational coefficient quadratic equation, the other root must be the conjugate, the square root of 5 + the square root of 3. The sum of the roots is 2 times the square root of 5, and the product is (the square root of 5)^2 - (the square root of 3)^2 = 5 - 3 = 2. The equation becomes x^2 - 2 times the square root of 5 x + 2 = 0, which is not listed among the options. Therefore, none of the above is the correct choice.

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