How many values of c in x^2 - 5x + c, result in rational roots which are integers?  Pick:
A) 23
B) 27
C) 25
D) 12
E) 82
Explanation:   By the quadratic formula, the roots of x2−5x+c=0x2−5x+c=0 are −(−5)±−52−4(1)(c)−−−−−−−−−−−√2(1)−(−5)±−52−4(1)(c)2(1) = 5±25−4c−−−−−−√25±25−4c2   To get rational roots, 25−4c25−4c should be square of an odd number. Why? because 5 + odd only divided by 2 perfectly.   Now let 25 - 4c = 1, then c = 6   If 25 - 4c = 9, then c = 4   If 25 - 4c = 25, then c = 0 and so on...   So infinite values are possible.   Answer:25
<result>C</result>
How many values of c in x^2 - 5x + c, result in rational roots which are integers?