Question

Question 4
Does there exist a quadratic equation whose coefficients are rational but both of its roots are irrational? Justify your answer.

Answer 1

Yes, consider the quadratic equation $2x^2$ + x – 4 = 0 with rational coefficients, the roots of the given quadratic are $\frac{-1+\sqrt{33}}{4}and\frac{-1-\sqrt{33}}{4}$ are irrational.