Multiple choice

Form the quadratic equation with rational coefficients whose one of the root is: $\sqrt3\, -\, \sqrt7$

  1. $y^{2}\, -\, 2\sqrt3y\, -\, 4\,  =\, 0$
  2. $y^{2}\, +\, 2\sqrt3y\, -\, 4\,  =\, 0$
  3. $y^{2}\, -\, 2\sqrt3y\, +\, 4\,  =\, 0$

  4. Equation with rational coefficient is not possible
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D Correct answer
AI explanation

For a quadratic equation to have rational coefficients, any irrational root must have its conjugate as the second root. Since the given root is √3 - √7, its conjugate is -√3 + √7 (or -√3 - √7 depending on the irrational part), but a quadratic equation can only have two roots. Forming an equation with both (√3 - √7) and (-√3 + √7) results in irrational coefficients for the x term, meaning an equation with strictly rational coefficients is not possible.

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