Problem: For a given value of kβ the product of the roots of x2β3kx+2k2β1=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 2k2β1.
β΄2k2β1=7,k2=4
Discriminant =(β3k)2β4β
1β
(2k2β1)=k2+4=8; the roots are irrational.