Problem: Let the roots of x2−3x+1=0 be r and s. Then the expression r2+s2 is:
Answer Choices:
A. a positive integer
B. a positive fraction greater than 1
C. a positive fraction less than 1
D. an irrational number
E. an imaginary number
Solution:
x2−3x+1=0∴rs=1 and r+s=3
∴(r+s)2=r2+2rs+s2=9∴ r2+s2=7