|
Question 252041: Find all possible integer values of k that make both x^2 + kx + 20 and
x^2+ kx - 28 factorable over the integers
Answer by jsmallt9(3758)   (Show Source):
You can put this solution on YOUR website! Factoring trinomials like these, with 1's in front of the squared terms, is a matter of finding the pair of factors of the constant term (at the end) which add up to the middle coefficient. Since the middle coefficient is k in both expressions, we want factors of the both constant terms that add up to the same number.
The factors of 20:
1 and 20 which add up to 21
2 and 10 which add up to 12
4 and 5 which add up to 9
-1 and -20 which add up to -21
-2 and -10 which add up to -12
-4 and -5 which add up to -9
The factors of -28:
1 and -28 which add up to -27
2 and -14 which add up to -12
4 and -7 which add up to -3
-1 and 28 which add up to 27
-2 and 14 which add up to 12
-4 and 7 which add up to 3
As you can see, there is are two sums of factors that is the same for both lists: 12 and -12. So these are the only possible values for k that will make both expressions factorable over the integers.
|
|
|
| |
