Problem: Consider x2+px+q=0 where p and q are positive numbers. If the roots of this equation differ by 1, then p equals
Answer Choices:
A. 4q+1​
B. q−1
C. −4q+1​
D. q+1
E. 4q−1​
Solution:
The roots are 21​(−p+p2−4q​) and 21​(−p−p2−4q​).
The difference is p2−4q​=1. Hence p2=4q+1 and p=4q+1​.