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Question
Does there exist a quadratic equation whose coefficients are rational but both of its roots are irrational? Justify your answer.
Solution
Yes, consider the quadratic equation 2x2 + x – 4 = 0 with rational coefficient.
The roots of the given quadratic equation are `(-1 + sqrt(33))/4` and `(-1 - sqrt(33))/4` are irrational.
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