Question

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

• A. Yes
• B. No
• C. Maybe
• D. Cannot be determined

Answer 1

The correct option is A Yes

Yes.

Let us consider the following example,

$x^2+6x+7=0$
$x=\frac{-6\pm \sqrt{6^2-4\left(1\right)\left(7\right)}}{2\left(1\right)}$
$x=\frac{-6\pm \sqrt{36-28}}{2}$

$x=\frac{-6\pm \sqrt{8}}{2}$
$x=\frac{-6\pm 2\sqrt{2}}{2}$
$x=-3\pm \sqrt{2}$