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