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Does there exist a quadratic equation whose coefficients are all distinct irrationals but both the roots are rationals? Why?

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Does there exist a quadratic equation whose coefficients are all distinct irrationals but both the roots are rationals? Why?
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Yes, consider the quadratic equation with all distinct irrationals coefficients i.e. `sqrt(3)x^(2)-7sqrt(3)x+12sqrt(3)=0`. The roots of this quadratic equation are 3 and 4, which are rationals.
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