Think of this as a discriminant question. For a quadratic equation ax^2 + bx + c = 0, first identify a = 1, b = -11, and c = -9. Now calculate D = b^2 - 4ac = (-11)^2 - 4(1)(-9) = 157. Since D > 0, the equation has two distinct real roots. Because it is positive but not a perfect square, the two real roots are irrational.