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 $2 x^{2}+x-4=$ Owith rational coefficient. The roots ofthe given quadratic equation are $\frac{-1+\sqrt{33}}{4}$
and $\frac{-1-\sqrt{33}}{4}$ are irrational.