Problem: For a given value of k​ the product of the roots of x2−3kx+2k2−1=0 is 7. The roots may be characterized as:
Answer Choices:
A. integral and positive
B. integral and negative
C. rational, but not integral
D. irrational
E. imaginary
Solution:
The product of the roots, here, is equal to 2k2−1.
∴2k2−1=7,k2=4
Discriminant =(−3k)2−4⋅1⋅(2k2−1)=k2+4=8; the roots are irrational.