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Does there exist a quadratic equation wh...

Does there exist a quadratic equation whose coefficients are rational but both of its roots are irrational? Justify you answer.

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Yes, consider the quadratic equation `2x^(2)+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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NCERT EXEMPLAR-QUADRIATIC EQUATIONS-Quadratic Equations
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  5. Is 0.2 a root of the equation x^(2)-0.4=0? Justify your answer.

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  16. Find the roots of the following quadratic equations by the factorisati...

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