2・12 For a known number $k$, the product of the roots of the equation $x^{2}-3 k x+2 k^{2}-1=0$ is 7, then all the roots are
(A) positive integers.
(B) negative integers.
(C) rational numbers but not integers.
(D) irrational numbers.
(E) imaginary numbers.
(11th American High School Mathematics Examination, 1960)
[Solution] By Vieta's formulas, we know $2 k^{2}-1=7$, which gives $k= \pm 2$. Therefore, the equation becomes
$$
x^{2} \pm 6 x+7=0,
$$
$$
x=3 \pm \sqrt{2} \text { or }-3 \pm \sqrt{2} \text {, }
$$

Thus, the answer is $(D)$.